diff --git a/lib/iris/analysis/calculus.py b/lib/iris/analysis/calculus.py
index 5dd9f39991..fb9f1f31e1 100644
--- a/lib/iris/analysis/calculus.py
+++ b/lib/iris/analysis/calculus.py
@@ -85,14 +85,16 @@ def _construct_midpoint_coord(coord, circular=None):
 
     """
     if circular and not hasattr(coord, 'circular'):
-        raise ValueError('Cannot produce circular midpoint from a coord '
-                         'without the circular attribute')
+        msg = ("Cannot produce a circular midpoint for the '{}' coord, "
+               "which does not have a 'circular' attribute.")
+        raise ValueError(msg.format(coord.name()))
 
     if circular is None:
         circular = getattr(coord, 'circular', False)
     elif circular != getattr(coord, 'circular', False):
-        warnings.warn('circular flag and Coord.circular attribute do '
-                      'not match')
+        msg = ("Construction coordinate midpoints for the '{}' coordinate, "
+               "though it has the attribute 'circular'={}.")
+        warnings.warn(msg.format(circular, coord.circular, coord.name()))
 
     if coord.ndim != 1:
         raise iris.exceptions.CoordinateMultiDimError(coord)