diff --git a/setup.cfg b/setup.cfg
index 71d63a395..e90b314cd 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -44,7 +44,7 @@ plugins =
 
 [coverage:report]
 precision = 2
-fail_under = 98.50
+fail_under = 98.80
 show_missing = true
 skip_covered = true
 exclude_lines =
diff --git a/tests/protocols/test_websocket.py b/tests/protocols/test_websocket.py
index c92de84b8..bb5c47c83 100644
--- a/tests/protocols/test_websocket.py
+++ b/tests/protocols/test_websocket.py
@@ -1,4 +1,5 @@
 import asyncio
+import typing
 
 import httpx
 import pytest
@@ -713,11 +714,22 @@ async def app(scope, receive, send):
         message = await receive()
         if message["type"] == "websocket.connect":
             await send_accept_task.wait()
-            await send({"type": "websocket.accept"})
         disconnect_message = await receive()
 
+    response: typing.Optional[httpx.Response] = None
+
     async def websocket_session(uri):
-        await websockets.client.connect(uri)
+        nonlocal response
+        async with httpx.AsyncClient() as client:
+            response = await client.get(
+                f"http://127.0.0.1:{unused_tcp_port}",
+                headers={
+                    "upgrade": "websocket",
+                    "connection": "upgrade",
+                    "sec-websocket-version": "13",
+                    "sec-websocket-key": "dGhlIHNhbXBsZSBub25jZQ==",
+                },
+            )
 
     config = Config(
         app=app,
@@ -731,9 +743,12 @@ async def websocket_session(uri):
             websocket_session(f"ws://127.0.0.1:{unused_tcp_port}")
         )
         await asyncio.sleep(0.1)
-        task.cancel()
         send_accept_task.set()
 
+    task.cancel()
+    assert response is not None
+    assert response.status_code == 500, response.text
+    assert response.text == "Internal Server Error"
     assert disconnect_message == {"type": "websocket.disconnect", "code": 1006}
 
 
@@ -744,6 +759,7 @@ async def test_send_close_on_server_shutdown(
     ws_protocol_cls, http_protocol_cls, unused_tcp_port: int
 ):
     disconnect_message = {}
+    server_shutdown_event = asyncio.Event()
 
     async def app(scope, receive, send):
         nonlocal disconnect_message
@@ -755,10 +771,13 @@ async def app(scope, receive, send):
                 disconnect_message = message
                 break
 
+    websocket: typing.Optional[websockets.client.WebSocketClientProtocol] = None
+
     async def websocket_session(uri):
-        async with websockets.client.connect(uri):
-            while True:
-                await asyncio.sleep(0.1)
+        nonlocal websocket
+        async with websockets.client.connect(uri) as ws_connection:
+            websocket = ws_connection
+            await server_shutdown_event.wait()
 
     config = Config(
         app=app,
@@ -773,7 +792,10 @@ async def websocket_session(uri):
         )
         await asyncio.sleep(0.1)
         disconnect_message_before_shutdown = disconnect_message
+    server_shutdown_event.set()
 
+    assert websocket is not None
+    assert websocket.close_code == 1012
     assert disconnect_message_before_shutdown == {}
     assert disconnect_message == {"type": "websocket.disconnect", "code": 1012}
     task.cancel()
diff --git a/uvicorn/protocols/websockets/websockets_impl.py b/uvicorn/protocols/websockets/websockets_impl.py
index d7650d179..297203ec6 100644
--- a/uvicorn/protocols/websockets/websockets_impl.py
+++ b/uvicorn/protocols/websockets/websockets_impl.py
@@ -90,7 +90,6 @@ def __init__(
         self.connect_sent = False
         self.lost_connection_before_handshake = False
         self.accepted_subprotocol: Optional[Subprotocol] = None
-        self.transfer_data_task: asyncio.Task = None  # type: ignore[assignment]
 
         self.ws_server: Server = Server()  # type: ignore[assignment]
 
@@ -145,6 +144,10 @@ def connection_lost(self, exc: Optional[Exception]) -> None:
 
     def shutdown(self) -> None:
         self.ws_server.closing = True
+        if self.handshake_completed_event.is_set():
+            self.fail_connection(1012)
+        else:
+            self.send_500_response()
         self.transport.close()
 
     def on_task_complete(self, task: asyncio.Task) -> None:
diff --git a/uvicorn/protocols/websockets/wsproto_impl.py b/uvicorn/protocols/websockets/wsproto_impl.py
index f2677e004..1d76f3a88 100644
--- a/uvicorn/protocols/websockets/wsproto_impl.py
+++ b/uvicorn/protocols/websockets/wsproto_impl.py
@@ -4,7 +4,6 @@
 import typing
 from urllib.parse import unquote
 
-import h11
 import wsproto
 from wsproto import ConnectionType, events
 from wsproto.connection import ConnectionState
@@ -232,17 +231,14 @@ def send_500_response(self) -> None:
             (b"content-type", b"text/plain; charset=utf-8"),
             (b"connection", b"close"),
         ]
-        if self.conn.connection is None:
-            output = self.conn.send(wsproto.events.RejectConnection(status_code=500))
-        else:
-            msg = h11.Response(
-                status_code=500, headers=headers, reason="Internal Server Error"
+        output = self.conn.send(
+            wsproto.events.RejectConnection(
+                status_code=500, headers=headers, has_body=True
             )
-            output = self.conn.send(msg)
-            msg = h11.Data(data=b"Internal Server Error")
-            output += self.conn.send(msg)
-            msg = h11.EndOfMessage()
-            output += self.conn.send(msg)
+        )
+        output += self.conn.send(
+            wsproto.events.RejectData(data=b"Internal Server Error")
+        )
         self.transport.write(output)
 
     async def run_asgi(self) -> None: