diff --git a/starlette/endpoints.py b/starlette/endpoints.py
index e27e4fe49..73367c257 100644
--- a/starlette/endpoints.py
+++ b/starlette/endpoints.py
@@ -17,6 +17,11 @@ def __init__(self, scope: Scope, receive: Receive, send: Send) -> None:
         self.scope = scope
         self.receive = receive
         self.send = send
+        self._allowed_methods = [
+            method
+            for method in ("GET", "HEAD", "POST", "PUT", "PATCH", "DELETE", "OPTIONS")
+            if getattr(self, method.lower(), None) is not None
+        ]
 
     def __await__(self) -> typing.Generator:
         return self.dispatch().__await__()
@@ -43,9 +48,10 @@ async def method_not_allowed(self, request: Request) -> Response:
         # If we're running inside a starlette application then raise an
         # exception, so that the configurable exception handler can deal with
         # returning the response. For plain ASGI apps, just return the response.
+        headers = {"Allow": ", ".join(self._allowed_methods)}
         if "app" in self.scope:
-            raise HTTPException(status_code=405)
-        return PlainTextResponse("Method Not Allowed", status_code=405)
+            raise HTTPException(status_code=405, headers=headers)
+        return PlainTextResponse("Method Not Allowed", status_code=405, headers=headers)
 
 
 class WebSocketEndpoint:
diff --git a/starlette/routing.py b/starlette/routing.py
index a7d72cb55..84ffcb3fb 100644
--- a/starlette/routing.py
+++ b/starlette/routing.py
@@ -250,10 +250,13 @@ def url_path_for(self, name: str, **path_params: typing.Any) -> URLPath:
 
     async def handle(self, scope: Scope, receive: Receive, send: Send) -> None:
         if self.methods and scope["method"] not in self.methods:
+            headers = {"Allow": ", ".join(self.methods)}
             if "app" in scope:
-                raise HTTPException(status_code=405)
+                raise HTTPException(status_code=405, headers=headers)
             else:
-                response = PlainTextResponse("Method Not Allowed", status_code=405)
+                response = PlainTextResponse(
+                    "Method Not Allowed", status_code=405, headers=headers
+                )
             await response(scope, receive, send)
         else:
             await self.app(scope, receive, send)
diff --git a/tests/test_endpoints.py b/tests/test_endpoints.py
index e57d47486..9895a4559 100644
--- a/tests/test_endpoints.py
+++ b/tests/test_endpoints.py
@@ -40,6 +40,7 @@ def test_http_endpoint_route_method(client):
     response = client.post("/")
     assert response.status_code == 405
     assert response.text == "Method Not Allowed"
+    assert response.headers["allow"] == "GET"
 
 
 def test_websocket_endpoint_on_connect(test_client_factory):
diff --git a/tests/test_routing.py b/tests/test_routing.py
index 231c581fb..dc28427ee 100644
--- a/tests/test_routing.py
+++ b/tests/test_routing.py
@@ -161,6 +161,7 @@ def test_router(client):
     response = client.post("/")
     assert response.status_code == 405
     assert response.text == "Method Not Allowed"
+    assert set(response.headers["allow"].split(", ")) == {"HEAD", "GET"}
 
     response = client.get("/foo")
     assert response.status_code == 404