diff --git a/Lib/fontTools/varLib/instancer/names.py b/Lib/fontTools/varLib/instancer/names.py
index dad3fd7e5..f9454688e 100644
--- a/Lib/fontTools/varLib/instancer/names.py
+++ b/Lib/fontTools/varLib/instancer/names.py
@@ -134,6 +134,14 @@ def updateNameTable(varfont, axisLimits):
 def checkAxisValuesExist(stat, axisValues, axisCoords):
     seen = set()
     designAxes = stat.DesignAxisRecord.Axis
+    hasValues = set()
+    for value in stat.AxisValueArray.AxisValue:
+        if value.Format in (1, 2, 3):
+            hasValues.add(designAxes[value.AxisIndex].AxisTag)
+        elif value.Format == 4:
+            for rec in value.AxisValueRecord:
+                hasValues.add(designAxes[rec.AxisIndex].AxisTag)
+
     for axisValueTable in axisValues:
         axisValueFormat = axisValueTable.Format
         if axisValueTable.Format in (1, 2, 3):
@@ -150,7 +158,7 @@ def checkAxisValuesExist(stat, axisValues, axisCoords):
                 if axisTag in axisCoords and rec.Value == axisCoords[axisTag]:
                     seen.add(axisTag)
 
-    missingAxes = set(axisCoords) - seen
+    missingAxes = (set(axisCoords) - seen) & hasValues
     if missingAxes:
         missing = ", ".join(f"'{i}': {axisCoords[i]}" for i in missingAxes)
         raise ValueError(f"Cannot find Axis Values {{{missing}}}")
diff --git a/Tests/varLib/instancer/names_test.py b/Tests/varLib/instancer/names_test.py
index 7aeee6547..0d7ef1a86 100644
--- a/Tests/varLib/instancer/names_test.py
+++ b/Tests/varLib/instancer/names_test.py
@@ -333,3 +333,21 @@ def test_updateNameTable_existing_subfamily_name_is_not_regular(varfont):
     instancer.names.updateNameTable(varfont, {"wght": 100})
     expected = {(2, 3, 1, 0x409): "Regular", (17, 3, 1, 0x409): "Thin"}
     _test_name_records(varfont, expected, isNonRIBBI=True)
+
+
+def test_name_irrelevant_axes(varfont):
+    # Cannot update name table if not on a named axis value location
+    with pytest.raises(ValueError) as excinfo:
+        location = {"wght": 400, "wdth": 90}
+        instance = instancer.instantiateVariableFont(
+            varfont, location, updateFontNames=True
+        )
+    assert "Cannot find Axis Values" in str(excinfo.value)
+
+    # Now let's make the wdth axis "irrelevant" to naming (no axis values)
+    varfont["STAT"].table.AxisValueArray.AxisValue.pop(6)
+    varfont["STAT"].table.AxisValueArray.AxisValue.pop(4)
+    location = {"wght": 400, "wdth": 90}
+    instance = instancer.instantiateVariableFont(
+        varfont, location, updateFontNames=True
+    )