diff --git a/docs/whats-new.rst b/docs/whats-new.rst
index 5c0e2803..71c06918 100644
--- a/docs/whats-new.rst
+++ b/docs/whats-new.rst
@@ -8,6 +8,9 @@ What's new
 - rewrite :py:meth:`Dataset.pint.quantify` and :py:meth:`DataArray.pint.quantify`,
   to use pint's `parse_units` instead of `parse_expression` (:pull:`40`)
   By `Tom Nicholas <https://github.com/TomNicholas>`_.
+- ensure the variable which causes the error is explicit if an error occurs in
+  :py:meth:`Dataset.pint.quantify` (:pull:`43`)
+  By `Tom Nicholas <https://github.com/TomNicholas>`_.
 - refactor the internal conversion functions (:pull:`56`)
   By `Justus Magin <https://github.com/keewis>`_.
 - allow converting indexes (except :py:class:`pandas.MultiIndex`) (:pull:`56`)
diff --git a/pint_xarray/accessors.py b/pint_xarray/accessors.py
index 15b0b7ee..d68833b4 100644
--- a/pint_xarray/accessors.py
+++ b/pint_xarray/accessors.py
@@ -1145,14 +1145,18 @@ def quantify(self, units=None, unit_registry=None, **unit_kwargs):
 
         unit_attrs = conversion.extract_unit_attributes(self.ds)
 
-        units = {
-            name: _decide_units(unit, registry, attr)
-            for name, (unit, attr) in zip_mappings(units, unit_attrs).items()
-            if unit is not None or attr is not None
-        }
-
+        possible_new_units = zip_mappings(units, unit_attrs)
+        new_units = {}
+        for name, (unit, attr) in possible_new_units.items():
+            if unit is not None or attr is not None:
+                try:
+                    new_units[name] = _decide_units(unit, registry, attr)
+                except Exception as e:
+                    raise ValueError(
+                        f"Failed to assign units to variable {name}"
+                    ) from e
         return self.ds.pipe(conversion.strip_unit_attributes).pipe(
-            conversion.attach_units, units
+            conversion.attach_units, new_units
         )
 
     def dequantify(self, format=None):
diff --git a/pint_xarray/tests/test_accessors.py b/pint_xarray/tests/test_accessors.py
index a7a22ef6..fc3d32d2 100644
--- a/pint_xarray/tests/test_accessors.py
+++ b/pint_xarray/tests/test_accessors.py
@@ -247,7 +247,12 @@ def test_error_when_already_units(self, example_quantity_ds):
 
     def test_error_on_nonsense_units(self, example_unitless_ds):
         ds = example_unitless_ds
-        with pytest.raises(UndefinedUnitError):
+        with pytest.raises(ValueError):
+            ds.pint.quantify(units={"users": "aecjhbav"})
+
+    def test_error_indicates_problematic_variable(self, example_unitless_ds):
+        ds = example_unitless_ds
+        with pytest.raises(ValueError, match="users"):
             ds.pint.quantify(units={"users": "aecjhbav"})