diff --git a/fastapi/dependencies/utils.py b/fastapi/dependencies/utils.py
index 4b69e39a1..a927dbb69 100644
--- a/fastapi/dependencies/utils.py
+++ b/fastapi/dependencies/utils.py
@@ -54,7 +54,7 @@ from fastapi.concurrency import (
     contextmanager_in_threadpool,
 )
 from fastapi.dependencies.models import Dependant, SecurityRequirement
-from fastapi.exceptions import DependencyScopeError
+from fastapi.exceptions import DependencyScopeError, FastAPIError
 from fastapi.logger import logger
 from fastapi.security.base import SecurityBase
 from fastapi.security.oauth2 import OAuth2, SecurityScopes
@@ -549,7 +549,24 @@ async def _solve_generator(
         cm = contextmanager_in_threadpool(contextmanager(dependant.call)(**sub_values))
     elif dependant.is_async_gen_callable:
         cm = asynccontextmanager(dependant.call)(**sub_values)
-    return await stack.enter_async_context(cm)
+
+    try:
+        solved = await stack.enter_async_context(cm)
+    except RuntimeError as ex:
+        if str(ex) != "generator didn't yield":
+            raise ex
+
+        dependency_name = getattr(call, "__name__", "(unknown)")
+        raise FastAPIError(
+            f"Dependency {dependency_name} raised: {ex}. There's a high chance that "
+            "this is a dependency with yield that has a block with a bare except, or a "
+            "block with except Exception, and is not raising the exception again. Read "
+            "more about it in the docs: "
+            "https://fastapi.tiangolo.com/tutorial/dependencies/dependencies-with-yield"
+            "/#dependencies-with-yield-and-except"
+        ) from ex
+
+    return solved
 
 
 @dataclass
diff --git a/tests/test_dependency_runtime_errors.py b/tests/test_dependency_runtime_errors.py
new file mode 100644
index 000000000..5dd45976e
--- /dev/null
+++ b/tests/test_dependency_runtime_errors.py
@@ -0,0 +1,29 @@
+import pytest
+from anyio import open_file
+from fastapi import Depends, FastAPI
+from fastapi.testclient import TestClient
+
+app = FastAPI()
+
+
+async def get_username():
+    try:
+        async with await open_file("/path/to/sanchez.txt", "r") as f:
+            yield await f.read()  # pragma: no cover
+    except OSError as ex:
+        raise RuntimeError("File something something, wubba lubba dub dub!") from ex
+
+
+@app.get("/me")
+def get_me(username: str = Depends(get_username)):
+    return username  # pragma: no cover
+
+
+client = TestClient(app)
+
+
+@pytest.mark.anyio
+def test_runtime_error():
+    with pytest.raises(RuntimeError) as exc_info:
+        client.get("/me")
+    assert "File something something" in exc_info.value.args[0]