diff --git a/CHANGELOG.md b/CHANGELOG.md
index 3ed17e02b2..40a12afb8d 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,6 +10,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ### Fixed
 - `DataArray` interpolation failure due to incorrect ordering of coordinates when interpolating with autograd tracers.
+- Error in `CustomSourceTime` when evaluating at a list of times entirely outside of the range of the envelope definition times.
 
 ## [2.7.2] - 2024-08-07
 
diff --git a/tests/test_components/test_source.py b/tests/test_components/test_source.py
index 3fbf84ddfb..e4f01a0e81 100644
--- a/tests/test_components/test_source.py
+++ b/tests/test_components/test_source.py
@@ -307,8 +307,20 @@ def test_custom_source_time(log_capture):
         atol=ATOL,
     )
 
+    # all times out of range
+    _ = cst.amp_time([-1])
+    _ = cst.amp_time(-1)
+    assert np.allclose(cst.amp_time([2]), np.exp(-1j * 2 * np.pi * 2 * freq0), rtol=0, atol=ATOL)
+
     assert_log_level(log_capture, None)
 
+    vals = td.components.data.data_array.TimeDataArray([1, 2], coords=dict(t=[-1, -0.5]))
+    dataset = td.components.data.dataset.TimeDataset(values=vals)
+    cst = td.CustomSourceTime(source_time_dataset=dataset, freq0=freq0, fwidth=0.1e12)
+    source = td.PointDipole(center=(0, 0, 0), source_time=cst, polarization="Ex")
+    with AssertLogLevel(log_capture, "WARNING", contains_str="defined at times"):
+        sim = sim.updated_copy(sources=[source])
+
     # test normalization warning
     with AssertLogLevel(log_capture, "WARNING"):
         sim = sim.updated_copy(normalize_index=0)
diff --git a/tidy3d/components/simulation.py b/tidy3d/components/simulation.py
index e500001f6e..a05da33f5f 100644
--- a/tidy3d/components/simulation.py
+++ b/tidy3d/components/simulation.py
@@ -3161,6 +3161,31 @@ def _post_init_validators(self) -> None:
         self._validate_no_structures_pml()
         self._validate_tfsf_nonuniform_grid()
         self._validate_nonlinear_specs()
+        self._validate_custom_source_time()
+
+    def _validate_custom_source_time(self):
+        """Warn if all simulation times are outside CustomSourceTime definition range."""
+        # skip this validation if tmesh can't be computed, for example because of unloaded
+        # custom media
+        try:
+            _ = self.tmesh
+        except pydantic.ValidationError:
+            return
+        for idx, source in enumerate(self.sources):
+            if isinstance(source.source_time, CustomSourceTime):
+                if source.source_time._all_outside_range(tmesh=self.tmesh):
+                    data_times = source.source_time.data_times
+                    mint = np.min(data_times)
+                    maxt = np.max(data_times)
+                    mintmesh = np.min(self.tmesh)
+                    maxtmesh = np.max(self.tmesh)
+                    log.warning(
+                        f"'CustomSourceTime' at 'sources[{idx}]' is defined at "
+                        "times which do not include any of the 'Simulation.tmesh'. "
+                        f"'CustomSourceTime' is defined in the time range "
+                        f"'({mint}, {maxt})'; 'Simulation.tmesh' covers the range "
+                        f"'({mintmesh}, {maxtmesh})'"
+                    )
 
     def _validate_no_structures_pml(self) -> None:
         """Ensure no structures terminate / have bounds inside of PML."""
diff --git a/tidy3d/components/source.py b/tidy3d/components/source.py
index 5a7a245c3e..d3c222e542 100644
--- a/tidy3d/components/source.py
+++ b/tidy3d/components/source.py
@@ -352,6 +352,27 @@ def from_values(
             source_time_dataset=source_time_dataset,
         )
 
+    @property
+    def data_times(self) -> ArrayFloat1D:
+        """Times of envelope definition."""
+        if self.source_time_dataset is None:
+            return []
+        data_times = self.source_time_dataset.values.coords["t"].values.squeeze()
+        return data_times
+
+    def _all_outside_range(self, tmesh: ArrayFloat1D) -> bool:
+        """Whether all tmesh are outside range of definition."""
+        # make time a numpy array for uniform handling
+        data_times = self.data_times
+
+        # shift time
+        twidth = 1.0 / (2 * np.pi * self.fwidth)
+        time_shifted = tmesh - self.offset * twidth
+
+        mask = (time_shifted < min(data_times)) | (time_shifted > max(data_times))
+
+        return all(mask)
+
     def amp_time(self, time: float) -> complex:
         """Complex-valued source amplitude as a function of time.
 
@@ -370,8 +391,8 @@ def amp_time(self, time: float) -> complex:
             return None
 
         # make time a numpy array for uniform handling
-        times = np.array([time] if isinstance(time, float) else time)
-        data_times = self.source_time_dataset.values.coords["t"].values.squeeze()
+        times = np.array([time] if isinstance(time, (int, float)) else time)
+        data_times = self.data_times
 
         # shift time
         twidth = 1.0 / (2 * np.pi * self.fwidth)
@@ -384,12 +405,13 @@ def amp_time(self, time: float) -> complex:
         envelope = np.zeros(len(time_shifted), dtype=complex)
         values = self.source_time_dataset.values
         envelope[mask] = values.sel(t=time_shifted[mask], method="nearest").to_numpy()
-        envelope[~mask] = values.interp(t=time_shifted[~mask]).to_numpy()
+        if not all(mask):
+            envelope[~mask] = values.interp(t=time_shifted[~mask]).to_numpy()
 
         # modulation, phase, amplitude
         omega0 = 2 * np.pi * self.freq0
         offset = np.exp(1j * self.phase)
-        oscillation = np.exp(-1j * omega0 * time)
+        oscillation = np.exp(-1j * omega0 * times)
         amp = self.amplitude
 
         return offset * oscillation * amp * envelope