diff --git a/pyproject.toml b/pyproject.toml
index fa298ad5b..e0f240bc5 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -247,6 +247,9 @@ omit = [
     "docs_src/response_model/tutorial003_04_py310.py",
     "docs_src/dependencies/tutorial013_an_py310.py",  # temporary code example?
     "docs_src/dependencies/tutorial014_an_py310.py",  # temporary code example?
+    # Only run (and cover) on Python 3.14+
+    "docs_src/dependencies/tutorial008_an_py310.py",
+    "tests/test_stringified_annotation_dependency_py314.py",
     # Pydantic v1 migration, no longer tested
     "docs_src/pydantic_v1_in_v2/tutorial001_an_py310.py",
     "docs_src/pydantic_v1_in_v2/tutorial002_an_py310.py",
diff --git a/tests/test_asyncapi.py b/tests/test_asyncapi.py
index 7000c4cf9..686cb8147 100644
--- a/tests/test_asyncapi.py
+++ b/tests/test_asyncapi.py
@@ -18,6 +18,10 @@ def test_asyncapi_schema():
         await websocket.close()
 
     client = TestClient(app)
+    with client.websocket_connect("/ws"):
+        pass
+    with client.websocket_connect("/ws/foo"):
+        pass
     response = client.get("/asyncapi.json")
     assert response.status_code == 200, response.text
     schema = response.json()
@@ -38,6 +42,9 @@ def test_asyncapi_no_websockets():
         return {"message": "Hello World"}
 
     client = TestClient(app)
+    response = client.get("/")
+    assert response.status_code == 200
+    assert response.json() == {"message": "Hello World"}
     response = client.get("/asyncapi.json")
     assert response.status_code == 200, response.text
     schema = response.json()
@@ -55,6 +62,9 @@ def test_asyncapi_caching():
         await websocket.accept()
         await websocket.close()
 
+    client = TestClient(app)
+    with client.websocket_connect("/ws"):
+        pass
     schema1 = app.asyncapi()
     schema2 = app.asyncapi()
     # Should return the same object (identity check)
@@ -71,6 +81,8 @@ def test_asyncapi_ui():
         await websocket.close()
 
     client = TestClient(app)
+    with client.websocket_connect("/ws"):
+        pass
     response = client.get("/asyncapi-docs")
     assert response.status_code == 200, response.text
     assert response.headers["content-type"] == "text/html; charset=utf-8"
@@ -88,6 +100,8 @@ def test_asyncapi_ui_navigation():
         await websocket.close()
 
     client = TestClient(app)
+    with client.websocket_connect("/ws"):
+        pass
     response = client.get("/asyncapi-docs")
     assert response.status_code == 200, response.text
     # Should contain link to OpenAPI docs
@@ -109,6 +123,11 @@ def test_swagger_ui_asyncapi_navigation():
         await websocket.close()
 
     client = TestClient(app)
+    response = client.get("/")
+    assert response.status_code == 200
+    assert response.json() == {"message": "Hello World"}
+    with client.websocket_connect("/ws"):
+        pass
     response = client.get("/docs")
     assert response.status_code == 200, response.text
     # Should contain link to AsyncAPI docs
@@ -131,6 +150,8 @@ def test_asyncapi_custom_urls():
         await websocket.close()
 
     client = TestClient(app)
+    with client.websocket_connect("/ws"):
+        pass
     # Test custom JSON endpoint
     response = client.get("/custom/asyncapi.json")
     assert response.status_code == 200, response.text
@@ -163,6 +184,8 @@ def test_asyncapi_disabled():
         await websocket.close()
 
     client = TestClient(app)
+    with client.websocket_connect("/ws"):
+        pass
     # Endpoints should return 404
     response = client.get("/asyncapi.json")
     assert response.status_code == 404
@@ -180,6 +203,8 @@ def test_asyncapi_channel_structure():
         await websocket.close()
 
     client = TestClient(app)
+    with client.websocket_connect("/ws"):
+        pass
     response = client.get("/asyncapi.json")
     assert response.status_code == 200, response.text
     schema = response.json()
@@ -209,6 +234,12 @@ def test_asyncapi_multiple_websockets():
         await websocket.close()
 
     client = TestClient(app)
+    with client.websocket_connect("/ws1"):
+        pass
+    with client.websocket_connect("/ws2"):
+        pass
+    with client.websocket_connect("/ws3/bar"):
+        pass
     response = client.get("/asyncapi.json")
     assert response.status_code == 200, response.text
     schema = response.json()
@@ -233,6 +264,8 @@ def test_asyncapi_with_metadata():
         await websocket.close()
 
     client = TestClient(app)
+    with client.websocket_connect("/ws"):
+        pass
     response = client.get("/asyncapi.json")
     assert response.status_code == 200, response.text
     schema = response.json()
@@ -256,6 +289,8 @@ def test_asyncapi_ui_no_docs_url():
         await websocket.close()
 
     client = TestClient(app)
+    with client.websocket_connect("/ws"):
+        pass
     response = client.get("/asyncapi-docs")
     assert response.status_code == 200, response.text
     # Should not contain link to /docs if docs_url is None
@@ -277,6 +312,8 @@ def test_asyncapi_with_servers():
         await websocket.close()
 
     client = TestClient(app)
+    with client.websocket_connect("/ws"):
+        pass
     response = client.get("/asyncapi.json")
     assert response.status_code == 200, response.text
     schema = response.json()
@@ -302,6 +339,8 @@ def test_asyncapi_with_all_metadata():
         await websocket.close()
 
     client = TestClient(app)
+    with client.websocket_connect("/ws"):
+        pass
     response = client.get("/asyncapi.json")
     assert response.status_code == 200, response.text
     schema = response.json()
@@ -337,6 +376,8 @@ def test_asyncapi_with_external_docs():
     }
 
     client = TestClient(app)
+    with client.websocket_connect("/ws"):
+        pass
     response = client.get("/asyncapi.json")
     assert response.status_code == 200, response.text
     schema = response.json()
@@ -357,6 +398,8 @@ def test_asyncapi_channel_with_route_name():
         await websocket.close()
 
     client = TestClient(app)
+    with client.websocket_connect("/ws"):
+        pass
     response = client.get("/asyncapi.json")
     assert response.status_code == 200, response.text
     schema = response.json()
@@ -376,6 +419,9 @@ def test_get_asyncapi_channel_direct():
         await websocket.accept()
         await websocket.close()
 
+    client = TestClient(app)
+    with client.websocket_connect("/ws"):
+        pass
     # Get the route from the app
     route = next(r for r in app.routes if isinstance(r, routing.APIWebSocketRoute))
     channel = get_asyncapi_channel(route=route)
@@ -394,6 +440,9 @@ def test_get_asyncapi_direct():
         await websocket.accept()
         await websocket.close()
 
+    client = TestClient(app)
+    with client.websocket_connect("/ws"):
+        pass
     schema = get_asyncapi(
         title=app.title,
         version=app.version,
@@ -419,6 +468,8 @@ def test_asyncapi_url_none_no_link_in_swagger():
         await websocket.close()
 
     client = TestClient(app)
+    with client.websocket_connect("/ws"):
+        pass
     # Swagger UI should not show AsyncAPI link when asyncapi_url is None
     response = client.get("/docs")
     assert response.status_code == 200, response.text
@@ -444,6 +495,8 @@ def test_asyncapi_with_root_path_in_servers():
 
     # Use TestClient with root_path to trigger the root_path logic
     client = TestClient(app, root_path="/api/v1")
+    with client.websocket_connect("/ws"):
+        pass
     response = client.get("/asyncapi.json")
     assert response.status_code == 200, response.text
     schema = response.json()
diff --git a/tests/test_dependencies_utils.py b/tests/test_dependencies_utils.py
index 9257d1c9e..54a21b348 100644
--- a/tests/test_dependencies_utils.py
+++ b/tests/test_dependencies_utils.py
@@ -1,4 +1,9 @@
-from fastapi.dependencies.utils import get_typed_annotation
+import inspect
+import sys
+from types import SimpleNamespace
+from unittest.mock import patch
+
+from fastapi.dependencies.utils import get_typed_annotation, get_typed_signature
 
 
 def test_get_typed_annotation():
@@ -6,3 +11,31 @@ def test_get_typed_annotation():
     annotation = "None"
     typed_annotation = get_typed_annotation(annotation, globals())
     assert typed_annotation is None
+
+
+def test_get_signature_nameerror_py314_branch():
+    """Cover _get_signature NameError branch with Python 3.14+ annotation_format path."""
+    real_signature = inspect.signature
+
+    def mock_signature(call, *args, **kwargs):
+        if kwargs.get("eval_str") is True:
+            raise NameError("undefined name")
+        # On Python < 3.14, inspect.signature does not accept annotation_format
+        kwargs.pop("annotation_format", None)
+        return real_signature(call, *args, **kwargs)
+
+    def simple_dep(x: int) -> int:
+        return x
+
+    # annotationlib is only available on Python 3.14+; provide a minimal mock  # noqa: E501
+    fake_annotationlib = SimpleNamespace(Format=SimpleNamespace(FORWARDREF=object()))
+
+    with (
+        patch.object(sys, "version_info", (3, 14)),
+        patch.dict("sys.modules", {"annotationlib": fake_annotationlib}),
+        patch("fastapi.dependencies.utils.inspect.signature", mock_signature),
+    ):
+        sig = get_typed_signature(simple_dep)
+    assert len(sig.parameters) == 1
+    assert sig.parameters["x"].annotation is int
+    assert simple_dep(42) == 42  # cover simple_dep body
diff --git a/tests/test_pydantic_v1_error.py b/tests/test_pydantic_v1_error.py
index 044fdf0d6..f02c9f78f 100644
--- a/tests/test_pydantic_v1_error.py
+++ b/tests/test_pydantic_v1_error.py
@@ -6,7 +6,7 @@ import pytest
 from tests.utils import skip_module_if_py_gte_314
 
 if sys.version_info >= (3, 14):
-    skip_module_if_py_gte_314()
+    skip_module_if_py_gte_314()  # pragma: no cover
 
 from fastapi import FastAPI
 from fastapi.exceptions import PydanticV1NotSupportedError
diff --git a/tests/utils.py b/tests/utils.py
index 09c4e13b0..3d1cfcf5b 100644
--- a/tests/utils.py
+++ b/tests/utils.py
@@ -12,5 +12,5 @@ needs_py314 = pytest.mark.skipif(
 
 def skip_module_if_py_gte_314():
     """Skip entire module on Python 3.14+ at import time."""
-    if sys.version_info >= (3, 14):
-        pytest.skip("requires python3.13-", allow_module_level=True)
+    if sys.version_info >= (3, 14):  # pragma: no cover
+        pytest.skip("requires python3.13-", allow_module_level=True)  # pragma: no cover