diff --git a/setup.cfg b/setup.cfg
index 46f4e3b99..ac52be52e 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -82,7 +82,7 @@ plugins =
 
 [coverage:report]
 precision = 2
-fail_under = 97.82
+fail_under = 97.92
 show_missing = true
 skip_covered = true
 exclude_lines =
diff --git a/tests/protocols/test_websocket.py b/tests/protocols/test_websocket.py
index a5fe93d5b..d495f5108 100644
--- a/tests/protocols/test_websocket.py
+++ b/tests/protocols/test_websocket.py
@@ -528,7 +528,6 @@ async def app(scope, receive, send):
         while True:
             message = await receive()
             if message["type"] == "websocket.connect":
-                print("accepted")
                 await send({"type": "websocket.accept"})
             elif message["type"] == "websocket.disconnect":
                 break
@@ -551,6 +550,66 @@ async def app(scope, receive, send):
     assert got_disconnect_event_before_shutdown is True
 
 
+@pytest.mark.anyio
+@pytest.mark.parametrize("ws_protocol_cls", WS_PROTOCOLS)
+@pytest.mark.parametrize("http_protocol_cls", HTTP_PROTOCOLS)
+async def test_not_accept_on_connection_lost(ws_protocol_cls, http_protocol_cls):
+    send_accept_task = asyncio.Event()
+
+    async def app(scope, receive, send):
+        while True:
+            message = await receive()
+            if message["type"] == "websocket.connect":
+                await send_accept_task.wait()
+                await send({"type": "websocket.accept"})
+            elif message["type"] == "websocket.disconnect":
+                break
+
+    async def websocket_session(uri):
+        async with websockets.client.connect(uri):
+            while True:
+                await asyncio.sleep(0.1)
+
+    config = Config(app=app, ws=ws_protocol_cls, http=http_protocol_cls, lifespan="off")
+    async with run_server(config):
+        task = asyncio.create_task(websocket_session("ws://127.0.0.1:8000"))
+        await asyncio.sleep(0.1)
+        task.cancel()
+        send_accept_task.set()
+
+
+@pytest.mark.anyio
+@pytest.mark.parametrize("ws_protocol_cls", WS_PROTOCOLS)
+@pytest.mark.parametrize("http_protocol_cls", HTTP_PROTOCOLS)
+async def test_send_close_on_server_shutdown(ws_protocol_cls, http_protocol_cls):
+    disconnect_message = {}
+
+    async def app(scope, receive, send):
+        nonlocal disconnect_message
+        while True:
+            message = await receive()
+            if message["type"] == "websocket.connect":
+                await send({"type": "websocket.accept"})
+            elif message["type"] == "websocket.disconnect":
+                disconnect_message = message
+                break
+
+    async def websocket_session(uri):
+        async with websockets.client.connect(uri):
+            while True:
+                await asyncio.sleep(0.1)
+
+    config = Config(app=app, ws=ws_protocol_cls, http=http_protocol_cls, lifespan="off")
+    async with run_server(config):
+        task = asyncio.create_task(websocket_session("ws://127.0.0.1:8000"))
+        await asyncio.sleep(0.1)
+        disconnect_message_before_shutdown = disconnect_message
+
+    assert disconnect_message_before_shutdown == {}
+    assert disconnect_message == {"type": "websocket.disconnect", "code": 1012}
+    task.cancel()
+
+
 @pytest.mark.anyio
 @pytest.mark.parametrize("ws_protocol_cls", WS_PROTOCOLS)
 @pytest.mark.parametrize("http_protocol_cls", HTTP_PROTOCOLS)
diff --git a/uvicorn/protocols/websockets/websockets_impl.py b/uvicorn/protocols/websockets/websockets_impl.py
index 01133b7e2..87e7baa36 100644
--- a/uvicorn/protocols/websockets/websockets_impl.py
+++ b/uvicorn/protocols/websockets/websockets_impl.py
@@ -345,6 +345,8 @@ async def asgi_receive(
             data = await self.recv()
         except ConnectionClosed as exc:
             self.closed_event.set()
+            if self.ws_server.closing:
+                return {"type": "websocket.disconnect", "code": 1012}
             return {"type": "websocket.disconnect", "code": exc.code}
 
         msg: WebSocketReceiveEvent = {  # type: ignore[typeddict-item]
diff --git a/uvicorn/protocols/websockets/wsproto_impl.py b/uvicorn/protocols/websockets/wsproto_impl.py
index 6e4f505f1..1f050f0a4 100644
--- a/uvicorn/protocols/websockets/wsproto_impl.py
+++ b/uvicorn/protocols/websockets/wsproto_impl.py
@@ -125,9 +125,12 @@ def resume_writing(self):
         self.writable.set()
 
     def shutdown(self):
-        self.queue.put_nowait({"type": "websocket.disconnect", "code": 1012})
-        output = self.conn.send(wsproto.events.CloseConnection(code=1012))
-        self.transport.write(output)
+        if self.handshake_complete:
+            self.queue.put_nowait({"type": "websocket.disconnect", "code": 1012})
+            output = self.conn.send(wsproto.events.CloseConnection(code=1012))
+            self.transport.write(output)
+        else:
+            self.send_500_response()
         self.transport.close()
 
     def on_task_complete(self, task):
@@ -222,9 +225,8 @@ def send_500_response(self):
     async def run_asgi(self):
         try:
             result = await self.app(self.scope, self.receive, self.send)
-        except BaseException as exc:
-            msg = "Exception in ASGI application\n"
-            self.logger.error(msg, exc_info=exc)
+        except BaseException:
+            self.logger.exception("Exception in ASGI application\n")
             if not self.handshake_complete:
                 self.send_500_response()
             self.transport.close()
@@ -257,14 +259,15 @@ async def send(self, message):
                 extensions = []
                 if self.config.ws_per_message_deflate:
                     extensions.append(PerMessageDeflate())
-                output = self.conn.send(
-                    wsproto.events.AcceptConnection(
-                        subprotocol=subprotocol,
-                        extensions=extensions,
-                        extra_headers=extra_headers,
+                if not self.transport.is_closing():
+                    output = self.conn.send(
+                        wsproto.events.AcceptConnection(
+                            subprotocol=subprotocol,
+                            extensions=extensions,
+                            extra_headers=extra_headers,
+                        )
                     )
-                )
-                self.transport.write(output)
+                    self.transport.write(output)
 
             elif message_type == "websocket.close":
                 self.queue.put_nowait({"type": "websocket.disconnect", "code": None})