diff --git a/scripts/tests/test_validate_docstrings.py b/scripts/tests/test_validate_docstrings.py
index 3d16fecb4ec3c..bb58449843096 100644
--- a/scripts/tests/test_validate_docstrings.py
+++ b/scripts/tests/test_validate_docstrings.py
@@ -633,6 +633,43 @@ def no_punctuation(self):
         """
         return "Hello world!"
 
+    def named_single_return(self):
+        """
+        Provides name but returns only one value.
+
+        Returns
+        -------
+        s : str
+           A nice greeting.
+        """
+        return "Hello world!"
+
+    def no_capitalization(self):
+        """
+        Forgets capitalization in return values description.
+
+        Returns
+        -------
+        foo : str
+           The first returned string.
+        bar : str
+           the second returned string.
+        """
+        return "Hello", "World!"
+
+    def no_period_multi(self):
+        """
+        Forgets period in return values description.
+
+        Returns
+        -------
+        foo : str
+           The first returned string
+        bar : str
+           The second returned string.
+        """
+        return "Hello", "World!"
+
 
 class BadSeeAlso(object):
 
@@ -829,10 +866,18 @@ def test_bad_generic_functions(self, capsys, func):
         ('BadReturns', 'yield_not_documented', ('No Yields section found',)),
         pytest.param('BadReturns', 'no_type', ('foo',),
                      marks=pytest.mark.xfail),
-        pytest.param('BadReturns', 'no_description', ('foo',),
-                     marks=pytest.mark.xfail),
-        pytest.param('BadReturns', 'no_punctuation', ('foo',),
-                     marks=pytest.mark.xfail),
+        ('BadReturns', 'no_description',
+         ('Return value has no description',)),
+        ('BadReturns', 'no_punctuation',
+         ('Return value description should finish with "."',)),
+        ('BadReturns', 'named_single_return',
+         ('The first line of the Returns section should contain only the '
+          'type, unless multiple values are being returned',)),
+        ('BadReturns', 'no_capitalization',
+         ('Return value description should start with a capital '
+          'letter',)),
+        ('BadReturns', 'no_period_multi',
+         ('Return value description should finish with "."',)),
         # Examples tests
         ('BadGenericDocStrings', 'method',
          ('Do not import numpy, as it is imported automatically',)),
diff --git a/scripts/validate_docstrings.py b/scripts/validate_docstrings.py
index bfc52a0de918b..4e389aed2b0d2 100755
--- a/scripts/validate_docstrings.py
+++ b/scripts/validate_docstrings.py
@@ -105,6 +105,11 @@
     'PR10': 'Parameter "{param_name}" requires a space before the colon '
             'separating the parameter name and type',
     'RT01': 'No Returns section found',
+    'RT02': 'The first line of the Returns section should contain only the '
+            'type, unless multiple values are being returned',
+    'RT03': 'Return value has no description',
+    'RT04': 'Return value description should start with a capital letter',
+    'RT05': 'Return value description should finish with "."',
     'YD01': 'No Yields section found',
     'SA01': 'See Also section not found',
     'SA02': 'Missing period at end of description for See Also '
@@ -685,8 +690,22 @@ def get_validation_data(doc):
                 errs.append(error('PR09', param_name=param))
 
     if doc.is_function_or_method:
-        if not doc.returns and 'return' in doc.method_source:
-            errs.append(error('RT01'))
+        if not doc.returns:
+            if 'return' in doc.method_source:
+                errs.append(error('RT01'))
+        else:
+            if len(doc.returns) == 1 and doc.returns[0][1]:
+                errs.append(error('RT02'))
+            for name_or_type, type_, desc in doc.returns:
+                if not desc:
+                    errs.append(error('RT03'))
+                else:
+                    desc = ' '.join(desc)
+                    if not desc[0].isupper():
+                        errs.append(error('RT04'))
+                    if not desc.endswith('.'):
+                        errs.append(error('RT05'))
+
         if not doc.yields and 'yield' in doc.method_source:
             errs.append(error('YD01'))