diff --git a/tests/test_server.py b/tests/test_server.py
index 5b9d9ba2d..c650be290 100644
--- a/tests/test_server.py
+++ b/tests/test_server.py
@@ -2,15 +2,23 @@
 
 import asyncio
 import contextlib
+import logging
 import signal
 import sys
 from typing import Callable, ContextManager, Generator
 
+import httpx
 import pytest
 
+from tests.utils import run_server
+from uvicorn._types import ASGIReceiveCallable, ASGISendCallable, Scope
 from uvicorn.config import Config
+from uvicorn.protocols.http.h11_impl import H11Protocol
+from uvicorn.protocols.http.httptools_impl import HttpToolsProtocol
 from uvicorn.server import Server
 
+pytestmark = pytest.mark.anyio
+
 
 # asyncio does NOT allow raising in signal handlers, so to detect
 # raised signals raised a mutable `witness` receives the signal
@@ -37,6 +45,12 @@ async def dummy_app(scope, receive, send):  # pragma: py-win32
     pass
 
 
+async def app(scope: Scope, receive: ASGIReceiveCallable, send: ASGISendCallable) -> None:
+    assert scope["type"] == "http"
+    await send({"type": "http.response.start", "status": 200, "headers": []})
+    await send({"type": "http.response.body", "body": b"", "more_body": False})
+
+
 if sys.platform == "win32":  # pragma: py-not-win32
     signals = [signal.SIGBREAK]
     signal_captures = [capture_signal_sync]
@@ -45,7 +59,6 @@ async def dummy_app(scope, receive, send):  # pragma: py-win32
     signal_captures = [capture_signal_sync, capture_signal_async]
 
 
-@pytest.mark.anyio
 @pytest.mark.parametrize("exception_signal", signals)
 @pytest.mark.parametrize("capture_signal", signal_captures)
 async def test_server_interrupt(
@@ -65,3 +78,16 @@ async def interrupt_running(srv: Server):
     assert witness
     # set by the server's graceful exit handler
     assert server.should_exit
+
+
+async def test_request_than_limit_max_requests_warn_log(
+    unused_tcp_port: int, http_protocol_cls: type[H11Protocol | HttpToolsProtocol], caplog: pytest.LogCaptureFixture
+):
+    caplog.set_level(logging.WARNING, logger="uvicorn.error")
+    config = Config(app=app, limit_max_requests=1, port=unused_tcp_port, http=http_protocol_cls)
+    async with run_server(config):
+        async with httpx.AsyncClient() as client:
+            tasks = [client.get(f"http://127.0.0.1:{unused_tcp_port}") for _ in range(2)]
+            responses = await asyncio.gather(*tasks)
+            assert len(responses) == 2
+    assert "Maximum request limit of 1 exceeded. Terminating process." in caplog.text
diff --git a/tools/cli_usage.py b/tools/cli_usage.py
index 5a9115710..1cfa88672 100644
--- a/tools/cli_usage.py
+++ b/tools/cli_usage.py
@@ -2,24 +2,26 @@
 Look for a marker comment in docs pages, and place the output of
 `$ uvicorn --help` there. Pass `--check` to ensure the content is in sync.
 """
+
+from __future__ import annotations
+
 import argparse
 import subprocess
 import sys
-import typing
 from pathlib import Path
 
 
-def _get_usage_lines() -> typing.List[str]:
+def _get_usage_lines() -> list[str]:
     res = subprocess.run(["uvicorn", "--help"], stdout=subprocess.PIPE)
     help_text = res.stdout.decode("utf-8")
     return ["```", "$ uvicorn --help", *help_text.splitlines(), "```"]
 
 
-def _find_next_codefence_lineno(lines: typing.List[str], after: int) -> int:
+def _find_next_codefence_lineno(lines: list[str], after: int) -> int:
     return next(lineno for lineno, line in enumerate(lines[after:], after) if line == "```")
 
 
-def _get_insert_location(lines: typing.List[str]) -> typing.Tuple[int, int]:
+def _get_insert_location(lines: list[str]) -> tuple[int, int]:
     marker = lines.index("<!-- :cli_usage: -->")
     start = marker + 1
 
diff --git a/uvicorn/server.py b/uvicorn/server.py
index fa7638b7d..f14026f16 100644
--- a/uvicorn/server.py
+++ b/uvicorn/server.py
@@ -250,8 +250,12 @@ async def on_tick(self, counter: int) -> bool:
         # Determine if we should exit.
         if self.should_exit:
             return True
-        if self.config.limit_max_requests is not None:
-            return self.server_state.total_requests >= self.config.limit_max_requests
+
+        max_requests = self.config.limit_max_requests
+        if max_requests is not None and self.server_state.total_requests >= max_requests:
+            logger.warning(f"Maximum request limit of {max_requests} exceeded. Terminating process.")
+            return True
+
         return False
 
     async def shutdown(self, sockets: list[socket.socket] | None = None) -> None: