diff --git a/tests/api/test_ratelimiting.py b/tests/api/test_ratelimiting.py
index a24638c9ef..a59e168db1 100644
--- a/tests/api/test_ratelimiting.py
+++ b/tests/api/test_ratelimiting.py
@@ -116,8 +116,9 @@ def test_allowed_via_ratelimit(self) -> None:
         # Should raise
         with self.assertRaises(LimitExceededError) as context:
             self.get_success_or_raise(
-                limiter.ratelimit(None, key="test_id", _time_now_s=5)
+                limiter.ratelimit(None, key="test_id", _time_now_s=5), by=0.5
             )
+
         self.assertEqual(context.exception.retry_after_ms, 5000)
 
         # Shouldn't raise
@@ -192,7 +193,7 @@ def test_allowed_via_ratelimit_and_overriding_parameters(self) -> None:
         # Second attempt, 1s later, will fail
         with self.assertRaises(LimitExceededError) as context:
             self.get_success_or_raise(
-                limiter.ratelimit(None, key=("test_id",), _time_now_s=1)
+                limiter.ratelimit(None, key=("test_id",), _time_now_s=1), by=0.5
             )
         self.assertEqual(context.exception.retry_after_ms, 9000)
 
diff --git a/tests/handlers/test_federation.py b/tests/handlers/test_federation.py
index b819b60c5d..3fe5b0a1b4 100644
--- a/tests/handlers/test_federation.py
+++ b/tests/handlers/test_federation.py
@@ -483,6 +483,7 @@ def create_invite() -> EventBase:
                 event.room_version,
             ),
             exc=LimitExceededError,
+            by=0.5,
         )
 
     def _build_and_send_join_event(
diff --git a/tests/handlers/test_room_member.py b/tests/handlers/test_room_member.py
index 3e28117e2c..2f7ebef7fe 100644
--- a/tests/handlers/test_room_member.py
+++ b/tests/handlers/test_room_member.py
@@ -70,6 +70,7 @@ def test_local_user_local_joins_contribute_to_limit_and_are_limited(self) -> Non
                 action=Membership.JOIN,
             ),
             LimitExceededError,
+            by=0.5,
         )
 
     @override_config({"rc_joins_per_room": {"per_second": 0, "burst_count": 2}})
@@ -206,6 +207,7 @@ def test_remote_joins_contribute_to_rate_limit(self) -> None:
                     remote_room_hosts=[self.OTHER_SERVER_NAME],
                 ),
                 LimitExceededError,
+                by=0.5,
             )
 
     # TODO: test that remote joins to a room are rate limited.
diff --git a/tests/unittest.py b/tests/unittest.py
index e6aad9ed40..18963b9e32 100644
--- a/tests/unittest.py
+++ b/tests/unittest.py
@@ -637,13 +637,13 @@ def get_success(self, d: Awaitable[TV], by: float = 0.0) -> TV:
         return self.successResultOf(deferred)
 
     def get_failure(
-        self, d: Awaitable[Any], exc: Type[_ExcType]
+        self, d: Awaitable[Any], exc: Type[_ExcType], by: float = 0.0
     ) -> _TypedFailure[_ExcType]:
         """
         Run a Deferred and get a Failure from it. The failure must be of the type `exc`.
         """
         deferred: Deferred[Any] = ensureDeferred(d)  # type: ignore[arg-type]
-        self.pump()
+        self.pump(by)
         return self.failureResultOf(deferred, exc)
 
     def get_success_or_raise(self, d: Awaitable[TV], by: float = 0.0) -> TV: