diff --git a/tests/protocols/test_http.py b/tests/protocols/test_http.py
index 6068d715..1ae45f40 100644
--- a/tests/protocols/test_http.py
+++ b/tests/protocols/test_http.py
@@ -775,6 +775,76 @@ async def test_shutdown_during_idle(http_protocol_cls: type[HTTPProtocol]):
     assert protocol.transport.is_closing()
 
 
+async def test_shutdown_during_streaming_sends_disconnect(http_protocol_cls: type[HTTPProtocol]):
+    """When the server shuts down during an SSE/streaming response,
+    receive() should return http.disconnect so the ASGI app can stop."""
+    got_disconnect_event = False
+
+    async def app(scope: Scope, receive: ASGIReceiveCallable, send: ASGISendCallable):
+        nonlocal got_disconnect_event
+
+        await send(
+            {
+                "type": "http.response.start",
+                "status": 200,
+                "headers": [(b"content-type", b"text/event-stream")],
+            }
+        )
+        await send({"type": "http.response.body", "body": b"data: hello\n\n", "more_body": True})
+
+        # This simulates an SSE app waiting for disconnect
+        message = await receive()
+        if message["type"] == "http.disconnect":
+            got_disconnect_event = True
+
+    protocol = get_connected_protocol(app, http_protocol_cls)
+    protocol.data_received(SIMPLE_GET_REQUEST)
+    # Trigger server shutdown while the app is streaming
+    protocol.shutdown()  # type: ignore[attr-defined]
+    await protocol.loop.run_one()
+    assert got_disconnect_event
+    assert b"HTTP/1.1 200 OK" in protocol.transport.buffer
+    assert b"data: hello" in protocol.transport.buffer
+    assert protocol.transport.is_closing()
+
+
+async def test_shutdown_during_streaming_allows_send_before_exit(http_protocol_cls: type[HTTPProtocol]):
+    """During server shutdown, the app should still be able to send() data
+    (e.g., a farewell SSE event) before returning."""
+    farewell_sent = False
+
+    async def app(scope: Scope, receive: ASGIReceiveCallable, send: ASGISendCallable):
+        nonlocal farewell_sent
+
+        await send(
+            {
+                "type": "http.response.start",
+                "status": 200,
+                "headers": [
+                    (b"content-type", b"text/event-stream"),
+                    (b"transfer-encoding", b"chunked"),
+                ],
+            }
+        )
+        await send({"type": "http.response.body", "body": b"data: hello\n\n", "more_body": True})
+
+        # Wait for disconnect
+        message = await receive()
+        assert message["type"] == "http.disconnect"
+
+        # Send a farewell event — this should still work since the transport is open
+        await send({"type": "http.response.body", "body": b"data: goodbye\n\n", "more_body": True})
+        farewell_sent = True
+
+    protocol = get_connected_protocol(app, http_protocol_cls)
+    protocol.data_received(SIMPLE_GET_REQUEST)
+    protocol.shutdown()  # type: ignore[attr-defined]
+    await protocol.loop.run_one()
+    assert farewell_sent
+    assert b"data: hello" in protocol.transport.buffer
+    assert b"data: goodbye" in protocol.transport.buffer
+
+
 async def test_100_continue_sent_when_body_consumed(http_protocol_cls: type[HTTPProtocol]):
     async def app(scope: Scope, receive: ASGIReceiveCallable, send: ASGISendCallable):
         body = b""
diff --git a/uvicorn/protocols/http/h11_impl.py b/uvicorn/protocols/http/h11_impl.py
index dd98269e..2ad140c8 100644
--- a/uvicorn/protocols/http/h11_impl.py
+++ b/uvicorn/protocols/http/h11_impl.py
@@ -344,6 +344,8 @@ class H11Protocol(asyncio.Protocol):
             self.transport.close()
         else:
             self.cycle.keep_alive = False
+            self.cycle.shutting_down = True
+            self.cycle.message_event.set()
 
     def pause_writing(self) -> None:
         """
@@ -397,6 +399,7 @@ class RequestResponseCycle:
         self.disconnected = False
         self.keep_alive = True
         self.waiting_for_100_continue = conn.they_are_waiting_for_100_continue
+        self.shutting_down = False
 
         # Request state
         self.body = bytearray()
@@ -429,8 +432,9 @@ class RequestResponseCycle:
                 self.logger.error(msg)
                 await self.send_500_response()
             elif not self.response_complete and not self.disconnected:
-                msg = "ASGI callable returned without completing response."
-                self.logger.error(msg)
+                if not self.shutting_down:
+                    msg = "ASGI callable returned without completing response."
+                    self.logger.error(msg)
                 self.transport.close()
         finally:
             self.on_response = lambda: None
@@ -528,12 +532,12 @@ class RequestResponseCycle:
             self.transport.write(output)
             self.waiting_for_100_continue = False
 
-        if not self.disconnected and not self.response_complete:
+        if not self.disconnected and not self.response_complete and not self.shutting_down:
             self.flow.resume_reading()
             await self.message_event.wait()
             self.message_event.clear()
 
-        if self.disconnected or self.response_complete:
+        if self.disconnected or self.response_complete or self.shutting_down:
             return {"type": "http.disconnect"}
 
         message: HTTPRequestEvent = {"type": "http.request", "body": bytes(self.body), "more_body": self.more_body}
diff --git a/uvicorn/protocols/http/httptools_impl.py b/uvicorn/protocols/http/httptools_impl.py
index 3aa354cc..a23c2fb6 100644
--- a/uvicorn/protocols/http/httptools_impl.py
+++ b/uvicorn/protocols/http/httptools_impl.py
@@ -349,6 +349,8 @@ class HttpToolsProtocol(asyncio.Protocol):
             self.transport.close()
         else:
             self.cycle.keep_alive = False
+            self.cycle.shutting_down = True
+            self.cycle.message_event.set()
 
     def pause_writing(self) -> None:
         """
@@ -400,6 +402,7 @@ class RequestResponseCycle:
         self.disconnected = False
         self.keep_alive = keep_alive
         self.waiting_for_100_continue = expect_100_continue
+        self.shutting_down = False
 
         # Request state
         self.body = bytearray()
@@ -434,8 +437,9 @@ class RequestResponseCycle:
                 self.logger.error(msg)
                 await self.send_500_response()
             elif not self.response_complete and not self.disconnected:
-                msg = "ASGI callable returned without completing response."
-                self.logger.error(msg)
+                if not self.shutting_down:
+                    msg = "ASGI callable returned without completing response."
+                    self.logger.error(msg)
                 self.transport.close()
         finally:
             self.on_response = lambda: None
@@ -560,12 +564,12 @@ class RequestResponseCycle:
             self.transport.write(b"HTTP/1.1 100 Continue\r\n\r\n")
             self.waiting_for_100_continue = False
 
-        if not self.disconnected and not self.response_complete:
+        if not self.disconnected and not self.response_complete and not self.shutting_down:
             self.flow.resume_reading()
             await self.message_event.wait()
             self.message_event.clear()
 
-        if self.disconnected or self.response_complete:
+        if self.disconnected or self.response_complete or self.shutting_down:
             return {"type": "http.disconnect"}
         message: HTTPRequestEvent = {"type": "http.request", "body": bytes(self.body), "more_body": self.more_body}
         self.body = bytearray()