diff --git a/starlette/websockets.py b/starlette/websockets.py
index fb76361c8..98396f30e 100644
--- a/starlette/websockets.py
+++ b/starlette/websockets.py
@@ -54,7 +54,9 @@ async def receive(self) -> Message:
                 self.client_state = WebSocketState.DISCONNECTED
             return message
         else:
-            raise RuntimeError('Cannot call "receive" once a disconnect message has been received.')
+            raise WebSocketDisconnect(
+                code=1006, reason='Cannot call "receive" once a disconnect message has been received.'
+            )
 
     async def send(self, message: Message) -> None:
         """
@@ -95,7 +97,7 @@ async def send(self, message: Message) -> None:
                 self.application_state = WebSocketState.DISCONNECTED
             await self._send(message)
         else:
-            raise RuntimeError('Cannot call "send" once a close message has been sent.')
+            raise WebSocketDisconnect(code=1006, reason='Cannot call "send" once a close message has been sent.')
 
     async def accept(
         self,
diff --git a/tests/test_websockets.py b/tests/test_websockets.py
index e76d8f29b..c6c32028d 100644
--- a/tests/test_websockets.py
+++ b/tests/test_websockets.py
@@ -449,9 +449,10 @@ async def app(scope: Scope, receive: Receive, send: Send) -> None:
         await websocket.close()
 
     client = test_client_factory(app)
-    with pytest.raises(RuntimeError):
+    with pytest.raises(WebSocketDisconnect) as exc:
         with client.websocket_connect("/"):
             pass  # pragma: no cover
+    assert exc.value.code == 1006
 
 
 def test_duplicate_disconnect(test_client_factory: TestClientFactory) -> None:
@@ -463,9 +464,10 @@ async def app(scope: Scope, receive: Receive, send: Send) -> None:
         message = await websocket.receive()
 
     client = test_client_factory(app)
-    with pytest.raises(RuntimeError):
+    with pytest.raises(WebSocketDisconnect) as exc:
         with client.websocket_connect("/") as websocket:
             websocket.close()
+    assert exc.value.code == 1006
 
 
 def test_websocket_scope_interface() -> None: