diff --git a/docs/src/whatsnew/latest.rst b/docs/src/whatsnew/latest.rst
index d0aefd02c1..25c0c5f3c9 100644
--- a/docs/src/whatsnew/latest.rst
+++ b/docs/src/whatsnew/latest.rst
@@ -79,6 +79,12 @@ This document explains the changes made to Iris for this release
 #. `@rcomer`_ removed some old redundant code that prevented determining the
    order of time cells. (:issue:`4697`, :pull:`4729`)
 
+#. `@stephenworsley`_ improved the accuracy of the error messages for
+   :meth:`~iris.cube.Cube.coord` when failing to find coordinates in the case where
+   a coordinate is given as the argument. Similarly, improved the error messages for
+   :meth:`~iris.cube.Cube.cell_measure` and :meth:`~iris.cube.Cube.ancillary_variable`.
+   (:issue:`4898`, :pull:`4928`)
+
 
 💣 Incompatible Changes
 =======================
diff --git a/lib/iris/cube.py b/lib/iris/cube.py
index 9779558506..4e24c099fe 100644
--- a/lib/iris/cube.py
+++ b/lib/iris/cube.py
@@ -1990,6 +1990,12 @@ def coord(
             if name_or_coord is not None:
                 if not isinstance(name_or_coord, str):
                     _name = name_or_coord.name()
+                    emsg = (
+                        "Expected to find exactly 1 coordinate matching the given "
+                        f"{_name!r} coordinate's metadata, but found none."
+                    )
+                    raise iris.exceptions.CoordinateNotFoundError(emsg)
+
             bad_name = _name or standard_name or long_name or ""
             emsg = (
                 f"Expected to find exactly 1 {bad_name!r} coordinate, "
@@ -2194,9 +2200,15 @@ def cell_measure(self, name_or_cell_measure=None):
                 bad_name = (
                     name_or_cell_measure and name_or_cell_measure.name()
                 ) or ""
+                if name_or_cell_measure is not None:
+                    emsg = (
+                        "Expected to find exactly 1 cell measure matching the given "
+                        f"{bad_name!r} cell measure's metadata, but found none."
+                    )
+                    raise iris.exceptions.CellMeasureNotFoundError(emsg)
             msg = (
-                "Expected to find exactly 1 %s cell_measure, but found "
-                "none." % bad_name
+                f"Expected to find exactly 1 {bad_name!r} cell measure, "
+                "but found none."
             )
             raise iris.exceptions.CellMeasureNotFoundError(msg)
 
@@ -2281,9 +2293,16 @@ def ancillary_variable(self, name_or_ancillary_variable=None):
                     name_or_ancillary_variable
                     and name_or_ancillary_variable.name()
                 ) or ""
+                if name_or_ancillary_variable is not None:
+                    emsg = (
+                        "Expected to find exactly 1 ancillary_variable matching the "
+                        f"given {bad_name!r} ancillary_variable's metadata, but found "
+                        "none."
+                    )
+                    raise iris.exceptions.AncillaryVariableNotFoundError(emsg)
             msg = (
-                "Expected to find exactly 1 {!s} ancillary_variable, but "
-                "found none.".format(bad_name)
+                f"Expected to find exactly 1 {bad_name!r} ancillary_variable, "
+                "but found none."
             )
             raise iris.exceptions.AncillaryVariableNotFoundError(msg)
 
diff --git a/lib/iris/tests/unit/cube/test_Cube.py b/lib/iris/tests/unit/cube/test_Cube.py
index 62c719aab9..7a6a200890 100644
--- a/lib/iris/tests/unit/cube/test_Cube.py
+++ b/lib/iris/tests/unit/cube/test_Cube.py
@@ -2528,6 +2528,25 @@ def test_fail_remove_ancilliary_variable_by_name(self):
             self.cube.remove_ancillary_variable("notname")
 
 
+class TestCoords(tests.IrisTest):
+    def setUp(self):
+        cube = Cube(np.arange(6).reshape(2, 3))
+        x_coord = DimCoord(points=np.array([2, 3, 4]), long_name="x")
+        cube.add_dim_coord(x_coord, 1)
+        self.x_coord = x_coord
+        self.cube = cube
+
+    def test_bad_coord(self):
+        bad_coord = self.x_coord.copy()
+        bad_coord.attributes = {"bad": "attribute"}
+        re = (
+            "Expected to find exactly 1 coordinate matching the given "
+            "'x' coordinate's metadata, but found none."
+        )
+        with self.assertRaisesRegex(CoordinateNotFoundError, re):
+            _ = self.cube.coord(bad_coord)
+
+
 class Test__getitem_CellMeasure(tests.IrisTest):
     def setUp(self):
         cube = Cube(np.arange(6).reshape(2, 3))