diff --git a/newsfragments/3562.bugfix.rst b/newsfragments/3562.bugfix.rst
new file mode 100644
index 0000000000..1d9a0e84ad
--- /dev/null
+++ b/newsfragments/3562.bugfix.rst
@@ -0,0 +1 @@
+Passing a NaN ``rate`` to :class:`trio.testing.MockClock` now raises :exc:`ValueError`, like a negative rate, instead of silently making the clock return NaN.
diff --git a/src/trio/_core/_mock_clock.py b/src/trio/_core/_mock_clock.py
index e437464b65..bc530115f5 100644
--- a/src/trio/_core/_mock_clock.py
+++ b/src/trio/_core/_mock_clock.py
@@ -1,5 +1,5 @@
 import time
-from math import inf
+from math import inf, isnan
 
 from .. import _core
 from .._abc import Clock
@@ -87,8 +87,8 @@ def rate(self) -> float:
 
     @rate.setter
     def rate(self, new_rate: float) -> None:
-        if new_rate < 0:
-            raise ValueError("rate must be >= 0")
+        if isnan(new_rate) or new_rate < 0:
+            raise ValueError(f"rate must be a non-negative number, not {new_rate!r}")
         else:
             real = self._real_clock()
             virtual = self._real_to_virtual(real)
diff --git a/src/trio/_core/_tests/test_mock_clock.py b/src/trio/_core/_tests/test_mock_clock.py
index 6131e7ba3f..47ee1ff2a4 100644
--- a/src/trio/_core/_tests/test_mock_clock.py
+++ b/src/trio/_core/_tests/test_mock_clock.py
@@ -28,10 +28,23 @@ def test_mock_clock() -> None:
     assert c.deadline_to_sleep_time(1.2) == 0
     assert c.deadline_to_sleep_time(1.3) > 999999
 
-    with pytest.raises(ValueError, match=r"^rate must be >= 0$"):
+    with pytest.raises(
+        ValueError, match=r"^rate must be a non-negative number, not -1$"
+    ):
         c.rate = -1
     assert c.rate == 0
 
+    with pytest.raises(
+        ValueError, match=r"^rate must be a non-negative number, not nan$"
+    ):
+        c.rate = float("nan")
+    assert c.rate == 0
+
+    with pytest.raises(
+        ValueError, match=r"^rate must be a non-negative number, not nan$"
+    ):
+        MockClock(rate=float("nan"))
+
     c.rate = 2
     assert c.current_time() == 1.2
     REAL_NOW += 1