  The quantum dynamics of the gravitational field non-minimally coupled to an
(also dynamical) scalar field is studied in the {\em broken phase}. For a
particular value of the coupling the system is classically conformal, and can
actually be understood as the group averaging of Einstein-Hilbert's action
under conformal transformations. Conformal invariance implies a simple Ward
identity asserting that the trace of the equation of motion for the graviton is
the equation of motion of the scalar field. We perform an explicit one-loop
computation to show that the DeWitt effective action is not UV divergent {\em
on shell} and to find that the Weyl symmetry Ward identity is preserved {\em on
shell} at that level. We also discuss the fate of this Ward identity at the
two-loop level --under the assumption that the two-loop UV divergent part of
the effective action can be retrieved from the Goroff-Sagnotti counterterm--
and show that its preservation in the renormalized theory requires the
introduction of counterterms which exhibit a logarithmic dependence on the
dilaton field.
