diff --git a/.github/workflows/test.yaml b/.github/workflows/test.yaml
index 614653d..c7b6927 100644
--- a/.github/workflows/test.yaml
+++ b/.github/workflows/test.yaml
@@ -24,7 +24,7 @@ jobs:
     runs-on: ubuntu-latest
     strategy:
       matrix:
-        python-version: ["3.7", "3.8", "3.9", "3.10", "3.11"]
+        python-version: ["3.7", "3.8", "3.9", "3.10", "3.11", "3.12"]
     steps:
     - uses: actions/checkout@v4
     - uses: actions/cache@v3
diff --git a/grpclib/server.py b/grpclib/server.py
index aebd34a..b652a75 100644
--- a/grpclib/server.py
+++ b/grpclib/server.py
@@ -625,6 +625,7 @@ class Server(_GC):
         self._config = config.__for_server__()
 
         self._server: Optional[asyncio.AbstractServer] = None
+        self._server_closed_fut: Optional[asyncio.Future[None]] = None
         self._handlers: Set[Handler] = set()
 
         self.__dispatch__ = _DispatchServerEvents()
@@ -703,7 +704,6 @@ class Server(_GC):
                 self._protocol_factory, path, sock=sock, backlog=backlog,
                 ssl=ssl
             )
-
         else:
             # FIXME: Not all union combinations were tried because there are
             #  too many unions
@@ -715,15 +715,18 @@ class Server(_GC):
                 backlog=backlog, ssl=ssl,
                 reuse_address=reuse_address, reuse_port=reuse_port
             )
+        self._server_closed_fut = self._loop.create_future()
 
     def close(self) -> None:
         """Stops accepting new connections, cancels all currently running
         requests. Request handlers are able to handle `CancelledError` and
         exit properly.
         """
-        if self._server is None:
+        if self._server is None or self._server_closed_fut is None:
             raise RuntimeError('Server is not started')
         self._server.close()
+        if not self._server_closed_fut.done():
+            self._server_closed_fut.set_result(None)
         for handler in self._handlers:
             handler.close()
 
@@ -731,8 +734,9 @@ class Server(_GC):
         """Coroutine to wait until all existing request handlers will exit
         properly.
         """
-        if self._server is None:
+        if self._server is None or self._server_closed_fut is None:
             raise RuntimeError('Server is not started')
+        await self._server_closed_fut
         await self._server.wait_closed()
         if self._handlers:
             await asyncio.wait({
diff --git a/grpclib/testing.py b/grpclib/testing.py
index 68d5000..99a93be 100644
--- a/grpclib/testing.py
+++ b/grpclib/testing.py
@@ -106,6 +106,7 @@ class ChannelFor:
             status_details_codec=self._status_details_codec,
         )
         self._server._server = _Server()
+        self._server._server_closed_fut = self._server._loop.create_future()
         self._server_protocol = self._server._protocol_factory()
 
         self._channel = Channel(
diff --git a/setup.cfg b/setup.cfg
index b5bcddb..535790c 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -52,6 +52,8 @@ asyncio_mode = auto
 filterwarnings =
     error
     ignore:.*pkg_resources.*:DeprecationWarning
+    ignore:.*google.*:DeprecationWarning
+    ignore:.*utcfromtimestamp.*:DeprecationWarning
     ignore::ResourceWarning
 
 [coverage:run]
diff --git a/tests/conn.py b/tests/conn.py
index 73f6795..fdd35bc 100644
--- a/tests/conn.py
+++ b/tests/conn.py
@@ -167,6 +167,6 @@ class ClientServer:
         return handler, stub
 
     async def __aexit__(self, *exc_info):
+        self.channel.close()
         self.server.close()
         await self.server.wait_closed()
-        self.channel.close()
diff --git a/tests/test_server.py b/tests/test_server.py
new file mode 100644
index 0000000..05a5ce3
--- /dev/null
+++ b/tests/test_server.py
@@ -0,0 +1,30 @@
+import asyncio
+
+import pytest
+
+from grpclib.server import Server
+
+
+async def serve_forever(server):
+    await server.start('127.0.0.1')
+    await server.wait_closed()
+
+
+@pytest.mark.asyncio
+async def test_wait_closed(loop: asyncio.AbstractEventLoop):
+    server = Server([])
+    task = loop.create_task(serve_forever(server))
+    done, pending = await asyncio.wait([task], timeout=0.1)
+    assert pending and not done
+    server.close()
+    done, pending = await asyncio.wait([task], timeout=0.1)
+    assert done and not pending
+
+
+@pytest.mark.asyncio
+async def test_close_twice():
+    server = Server([])
+    await server.start('127.0.0.1')
+    server.close()
+    server.close()
+    await server.wait_closed()