diff --git a/pyomo/core/plugins/transform/scaling.py b/pyomo/core/plugins/transform/scaling.py
index 0835e5fd060..d449d479475 100644
--- a/pyomo/core/plugins/transform/scaling.py
+++ b/pyomo/core/plugins/transform/scaling.py
@@ -9,6 +9,7 @@
 #  This software is distributed under the 3-clause BSD License.
 #  ___________________________________________________________________________
 
+import logging
 from pyomo.common.collections import ComponentMap
 from pyomo.core.base import Block, Var, Constraint, Objective, Suffix, value
 from pyomo.core.plugins.transform.hierarchy import Transformation
@@ -17,6 +18,8 @@
 from pyomo.core.expr import replace_expressions
 from pyomo.util.components import rename_components
 
+logger = logging.getLogger("pyomo.core.plugins.transform.scaling")
+
 
 @TransformationFactory.register(
     'core.scale_model', doc="Scale model variables, constraints, and objectives."
@@ -26,7 +29,7 @@ class ScaleModel(Transformation):
     Transformation to scale a model.
 
     This plugin performs variable, constraint, and objective scaling on
-    a model based on the scaling factors in the suffix 'scaling_parameter'
+    a model based on the scaling factors in the suffix 'scaling_factor'
     set for the variables, constraints, and/or objective. This is typically
     done to scale the problem for improved numerical properties.
 
@@ -35,6 +38,10 @@ class ScaleModel(Transformation):
         * :py:meth:`create_using <pyomo.core.plugins.transform.scaling.ScaleModel.create_using>`
         * :py:meth:`propagate_solution <pyomo.core.plugins.transform.scaling.ScaleModel.propagate_solution>`
 
+    By default, scaling components are renamed with the prefix ``scaled_``. To disable
+    this behavior and scale variables in-place (or keep the same names in a new model),
+    use the ``rename=False`` argument to ``apply_to`` or ``create_using``.
+
 
     Examples
     --------
@@ -67,8 +74,6 @@ class ScaleModel(Transformation):
         >>> print(value(scaled_model.scaled_obj))
         101.0
 
-    .. todo:: Implement an option to change the variables names or not
-
     """
 
     def __init__(self, **kwds):
@@ -308,10 +313,18 @@ def propagate_solution(self, scaled_model, original_model):
             original_v = original_model.find_component(original_v_path)
 
             for k in scaled_v:
-                original_v[k].set_value(
-                    value(scaled_v[k]) / component_scaling_factor_map[scaled_v[k]],
-                    skip_validation=True,
-                )
+                if scaled_v[k].value is None and original_v[k].value is not None:
+                    logger.warning(
+                        "Variable with value None in the scaled model is replacing"
+                        f" value of variable {original_v[k].name} in the original"
+                        f" model with None (was {original_v[k].value})."
+                    )
+                    original_v[k].set_value(None, skip_validation=True)
+                elif scaled_v[k].value is not None:
+                    original_v[k].set_value(
+                        value(scaled_v[k]) / component_scaling_factor_map[scaled_v[k]],
+                        skip_validation=True,
+                    )
                 if check_reduced_costs and scaled_v[k] in scaled_model.rc:
                     original_model.rc[original_v[k]] = (
                         scaled_model.rc[scaled_v[k]]
diff --git a/pyomo/core/tests/transform/test_scaling.py b/pyomo/core/tests/transform/test_scaling.py
index 7168f6bb707..94798535e9c 100644
--- a/pyomo/core/tests/transform/test_scaling.py
+++ b/pyomo/core/tests/transform/test_scaling.py
@@ -10,10 +10,12 @@
 #  ___________________________________________________________________________
 #
 
+import io
 import pyomo.common.unittest as unittest
 import pyomo.environ as pyo
 from pyomo.opt.base.solvers import UnknownSolver
 from pyomo.core.plugins.transform.scaling import ScaleModel, SuffixFinder
+from pyomo.common.log import LoggingIntercept
 
 
 class TestScaleModelTransformation(unittest.TestCase):
@@ -708,6 +710,31 @@ def test_get_float_scaling_factor_intermediate_level(self):
         # v2 should get SF from highest level, ignoring b3 level
         self.assertEqual(_finder.find(m.b1.b2.b3.v3), 0.3)
 
+    def test_propagate_solution_uninitialized_variable(self):
+        m = pyo.ConcreteModel()
+        m.x = pyo.Var([1, 2], initialize=1.0)
+        m.scaling_factor = pyo.Suffix(direction=pyo.Suffix.EXPORT)
+        m.scaling_factor[m.x[1]] = 10.0
+        m.scaling_factor[m.x[2]] = 10.0
+        scaled_model = pyo.TransformationFactory("core.scale_model").create_using(m)
+        scaled_model.scaled_x[1] = 20.0
+        scaled_model.scaled_x[2] = None
+
+        OUTPUT = io.StringIO()
+        with LoggingIntercept(OUTPUT, "pyomo.core.plugins.transform.scaling"):
+            pyo.TransformationFactory("core.scale_model").propagate_solution(
+                scaled_model, m
+            )
+        msg = (
+            "Variable with value None in the scaled model is replacing value of"
+            " variable x[2] in the original model with None (was 1.0).\n"
+        )
+        self.assertEqual(OUTPUT.getvalue(), msg)
+        self.assertAlmostEqual(m.x[1].value, 2.0, delta=1e-8)
+        # Note that value of x[2] in original model *has* been overridden to None.
+        # In this case, a warning has been raised.
+        self.assertIs(m.x[2].value, None)
+
 
 if __name__ == "__main__":
     unittest.main()