diff --git a/docs/src/whatsnew/latest.rst b/docs/src/whatsnew/latest.rst
index ebab20c806..574689ddee 100644
--- a/docs/src/whatsnew/latest.rst
+++ b/docs/src/whatsnew/latest.rst
@@ -58,6 +58,11 @@ This document explains the changes made to Iris for this release
 #. `@rcomer`_ added handling for string stash codes when saving pp files.
    (:issue:`6239`, :pull:`6289`)
 
+#. `@trexfeathers`_ and `@jrackham-mo`_ added a check for dtype castability when
+   saving NetCDF ``valid_range``, ``valid_min`` and ``valid_max`` attributes -
+   older NetCDF formats e.g. ``NETCDF4_CLASSIC`` support a maximum precision of
+   32-bit. (:issue:`6178`, :pull:`6343`)
+
 
 💣 Incompatible Changes
 =======================
@@ -70,7 +75,7 @@ This document explains the changes made to Iris for this release
 🚀 Performance Enhancements
 ===========================
 
-#. `@bouweandela`_ made loading :class:`~iris.cube.Cube`s from NetCDF files
+#. `@bouweandela`_ made loading :class:`~iris.cube.Cube`\s from NetCDF files
    faster. (:pull:`6229` and :pull:`6252`)
 
 #. `@fnattino`_ enabled lazy cube interpolation using the linear and
diff --git a/lib/iris/fileformats/netcdf/saver.py b/lib/iris/fileformats/netcdf/saver.py
index fa434bd439..6badeb6a0b 100644
--- a/lib/iris/fileformats/netcdf/saver.py
+++ b/lib/iris/fileformats/netcdf/saver.py
@@ -655,8 +655,7 @@ def write(
                 msg = "cf_profile is available but no {} defined.".format("cf_patch")
                 warnings.warn(msg, category=iris.warnings.IrisCfSaveWarning)
 
-    @staticmethod
-    def check_attribute_compliance(container, data_dtype):
+    def check_attribute_compliance(self, container, data_dtype):
         """Check attributte complliance."""
 
         def _coerce_value(val_attr, val_attr_value, data_dtype):
@@ -681,6 +680,7 @@ def _coerce_value(val_attr, val_attr_value, data_dtype):
             val_attr_value = container.attributes.get(val_attr)
             if val_attr_value is not None:
                 val_attr_value = np.asarray(val_attr_value)
+                self._ensure_valid_dtype(val_attr_value, val_attr, val_attr_value)
                 if data_dtype.itemsize == 1:
                     # Allow signed integral type
                     if val_attr_value.dtype.kind == "i":
diff --git a/lib/iris/tests/unit/fileformats/netcdf/saver/test_Saver.py b/lib/iris/tests/unit/fileformats/netcdf/saver/test_Saver.py
index 1c57323301..890e706c05 100644
--- a/lib/iris/tests/unit/fileformats/netcdf/saver/test_Saver.py
+++ b/lib/iris/tests/unit/fileformats/netcdf/saver/test_Saver.py
@@ -601,9 +601,11 @@ def assertAttribute(self, value):
             np.asarray(self.container.attributes[self.attribute]).dtype, value
         )
 
-    def check_attribute_compliance_call(self, value):
+    def check_attribute_compliance_call(self, value, file_type="NETCDF4"):
         self.set_attribute(value)
-        with Saver("nonexistent test file", "NETCDF4") as saver:
+        with Saver("nonexistent test file", file_type) as saver:
+            # Get the Mock to work properly.
+            saver._dataset.file_format = file_type
             saver.check_attribute_compliance(self.container, self.data_dtype)
 
 
@@ -638,6 +640,12 @@ def test_valid_range_not_numpy_array(self):
         self.check_attribute_compliance_call(value)
         self.assertAttribute(np.int64)
 
+    def test_uncastable_dtype(self):
+        self.data_dtype = np.dtype("int64")
+        value = [0, np.iinfo(self.data_dtype).max]
+        with self.assertRaisesRegex(ValueError, "cannot be safely cast"):
+            self.check_attribute_compliance_call(value, file_type="NETCDF4_CLASSIC")
+
 
 class Test_check_attribute_compliance__valid_min(
     _Common__check_attribute_compliance, tests.IrisTest
@@ -670,6 +678,12 @@ def test_valid_range_not_numpy_array(self):
         self.check_attribute_compliance_call(value)
         self.assertAttribute(np.int64)
 
+    def test_uncastable_dtype(self):
+        self.data_dtype = np.dtype("int64")
+        value = np.iinfo(self.data_dtype).min
+        with self.assertRaisesRegex(ValueError, "cannot be safely cast"):
+            self.check_attribute_compliance_call(value, file_type="NETCDF4_CLASSIC")
+
 
 class Test_check_attribute_compliance__valid_max(
     _Common__check_attribute_compliance, tests.IrisTest
@@ -702,6 +716,12 @@ def test_valid_range_not_numpy_array(self):
         self.check_attribute_compliance_call(value)
         self.assertAttribute(np.int64)
 
+    def test_uncastable_dtype(self):
+        self.data_dtype = np.dtype("int64")
+        value = np.iinfo(self.data_dtype).max
+        with self.assertRaisesRegex(ValueError, "cannot be safely cast"):
+            self.check_attribute_compliance_call(value, file_type="NETCDF4_CLASSIC")
+
 
 class Test_check_attribute_compliance__exception_handling(
     _Common__check_attribute_compliance, tests.IrisTest