diff --git a/esmvalcore/cmor/check.py b/esmvalcore/cmor/check.py
index cbab6d420b..52c5d19806 100644
--- a/esmvalcore/cmor/check.py
+++ b/esmvalcore/cmor/check.py
@@ -332,9 +332,10 @@ def _check_multiple_coords_same_stdname(self):
 
     def _check_dim_names(self):
         """Check dimension names."""
-        for (_, coordinate) in self._cmor_var.coordinates.items():
+        cmor_var_coordinates = self._cmor_var.coordinates.copy()
+        for (key, coordinate) in cmor_var_coordinates.items():
             if coordinate.generic_level:
-                continue
+                self._check_generic_level_dim_names(key, coordinate)
             else:
                 try:
                     cube_coord = self._cube.coord(var_name=coordinate.out_name)
@@ -383,11 +384,59 @@ def _check_dim_names(self):
                             self.report_error(
                                 self._does_msg, coordinate.name, 'exist')
 
+    def _check_generic_level_dim_names(self, key, coordinate):
+        if coordinate.generic_lev_coords:
+            for coord in coordinate.generic_lev_coords.values():
+                try:
+                    cube_coord = self._cube.coord(
+                        var_name=coord.out_name
+                    )
+                    coordinate.out_name = coord.out_name
+                    if cube_coord.standard_name == coord.standard_name:
+                        coordinate.standard_name = coord.standard_name
+                        coordinate.name = coord.name
+                except iris.exceptions.CoordinateNotFoundError:
+                    try:
+                        cube_coord = self._cube.coord(
+                            var_name=coord.standard_name
+                        )
+                        coordinate.standard_name = coord.standard_name
+                        coordinate.name = coord.name
+                    except iris.exceptions.CoordinateNotFoundError:
+                        pass
+            if coordinate.standard_name:
+                if not coordinate.out_name:
+                    self.report_error(
+                        f'Coordinate {coordinate.name} '
+                        'has wrong var_name.',
+                    )
+                level = coordinate.generic_lev_coords[coordinate.name]
+                level.generic_level = True
+                level.generic_lev_coords = self._cmor_var.coordinates[
+                    key].generic_lev_coords
+                self._cmor_var.coordinates[key] = level
+                self.report_debug_message(
+                    f'Generic level coordinate {key} '
+                    'will be checked against '
+                    f'{coordinate.name} coordinate information'
+                )
+            else:
+                if coordinate.out_name:
+                    self.report_critical(
+                        f'Coordinate {coordinate.name} '
+                        'has wrong standard_name '
+                        'or is not set.',
+                    )
+                else:
+                    self.report_critical(
+                        self._does_msg, coordinate.name, 'exist'
+                    )
+
     def _check_coords(self):
         """Check coordinates."""
         for coordinate in self._cmor_var.coordinates.values():
             # Cannot check generic_level coords as no CMOR information
-            if coordinate.generic_level:
+            if coordinate.generic_level and not coordinate.out_name:
                 continue
             var_name = coordinate.out_name
 
diff --git a/esmvalcore/cmor/table.py b/esmvalcore/cmor/table.py
index bba016f4d0..ca77c01d1e 100644
--- a/esmvalcore/cmor/table.py
+++ b/esmvalcore/cmor/table.py
@@ -325,7 +325,10 @@ def _assign_dimensions(self, var, generic_levels):
             if dimension in generic_levels:
                 coord = CoordinateInfo(dimension)
                 coord.generic_level = True
-                coord.axis = 'Z'
+                for name in self.coords:
+                    generic_level = self.coords[name].generic_lev_name
+                    if dimension in [generic_level]:
+                        coord.generic_lev_coords[name] = self.coords[name]
             else:
                 try:
                     coord = self.coords[dimension]
@@ -577,6 +580,7 @@ def __init__(self, name):
         super(CoordinateInfo, self).__init__()
         self.name = name
         self.generic_level = False
+        self.generic_lev_coords = {}
 
         self.axis = ""
         """Axis"""
@@ -606,6 +610,8 @@ def __init__(self, name):
         """Maximum allowed value"""
         self.must_have_bounds = ""
         """Whether bounds are required on this dimension"""
+        self.generic_lev_name = ""
+        """Generic level name"""
 
     def read_json(self, json_data):
         """
@@ -634,6 +640,7 @@ def read_json(self, json_data):
         self.valid_max = self._read_json_variable('valid_max')
         self.requested = self._read_json_list_variable('requested')
         self.must_have_bounds = self._read_json_variable('must_have_bounds')
+        self.generic_lev_name = self._read_json_variable('generic_level_name')
 
 
 class CMIP5Info(InfoBase):
diff --git a/tests/unit/cmor/test_cmor_check.py b/tests/unit/cmor/test_cmor_check.py
index 63006a7782..045fc5c22d 100644
--- a/tests/unit/cmor/test_cmor_check.py
+++ b/tests/unit/cmor/test_cmor_check.py
@@ -73,6 +73,8 @@ def __init__(self, name):
         self.stored_direction = "increasing"
         self.must_have_bounds = "yes"
         self.requested = []
+        self.generic_lev_coords = {}
+        self.generic_lev_name = ""
 
         valid_limits = {'lat': ('-90', '90'), 'lon': ('0', '360')}
         if name in valid_limits:
@@ -292,6 +294,20 @@ def test_rank_unstructured_grid(self):
         self.cube.add_aux_coord(new_lat, 1)
         self._check_cube()
 
+    def test_bad_generic_level(self):
+        """Test check fails in metadata if generic level coord
+        has wrong var_name."""
+        depth_coord = CoordinateInfoMock('depth')
+        depth_coord.axis = 'Z'
+        depth_coord.generic_lev_name = 'olevel'
+        depth_coord.out_name = 'lev'
+        depth_coord.name = 'depth_coord'
+        depth_coord.long_name = 'ocean depth coordinate'
+        self.var_info.coordinates['depth'].generic_lev_coords = {
+            'depth_coord': depth_coord}
+        self.var_info.coordinates['depth'].out_name = ""
+        self._check_fails_in_metadata()
+
     def test_check_bad_var_standard_name_strict_flag(self):
         """Test check fails for a bad variable standard_name with
         --cmor-check strict."""