diff --git a/homeassistant/components/sensor/__init__.py b/homeassistant/components/sensor/__init__.py
index 2bbcf3b119d..2c0d75ff471 100644
--- a/homeassistant/components/sensor/__init__.py
+++ b/homeassistant/components/sensor/__init__.py
@@ -404,10 +404,10 @@ class SensorEntity(Entity):
                     value = value.astimezone(timezone.utc)
 
                 return value.isoformat(timespec="seconds")
-            except (AttributeError, TypeError) as err:
+            except (AttributeError, OverflowError, TypeError) as err:
                 raise ValueError(
-                    f"Invalid datetime: {self.entity_id} has a timestamp device class "
-                    f"but does not provide a datetime state but {type(value)}"
+                    f"Invalid datetime: {self.entity_id} has timestamp device class "
+                    f"but provides state {value}:{type(value)} resulting in '{err}'"
                 ) from err
 
         # Received a date value
@@ -419,8 +419,8 @@ class SensorEntity(Entity):
                 return value.isoformat()
             except (AttributeError, TypeError) as err:
                 raise ValueError(
-                    f"Invalid date: {self.entity_id} has a date device class "
-                    f"but does not provide a date state but {type(value)}"
+                    f"Invalid date: {self.entity_id} has date device class "
+                    f"but provides state {value}:{type(value)} resulting in '{err}'"
                 ) from err
 
         if (
diff --git a/tests/components/sensor/test_init.py b/tests/components/sensor/test_init.py
index 4a3d0202c91..0bae8235ff9 100644
--- a/tests/components/sensor/test_init.py
+++ b/tests/components/sensor/test_init.py
@@ -183,8 +183,8 @@ async def test_deprecated_datetime_str(
     await hass.async_block_till_done()
 
     assert (
-        f"Invalid {provides}: sensor.test has a {device_class} device class "
-        f"but does not provide a {provides} state but {type(state_value)}"
+        f"Invalid {provides}: sensor.test has {device_class} device class "
+        f"but provides state {state_value}:{type(state_value)}"
     ) in caplog.text