In continuum reaction field models of solvation, unconstrained quantum mechanical calculation of the solute electronic structure inevitably leads to penetration of some solute charge density outside the cavity and into the solvent dielectric region. This produces a rarely recognized or treated volume polarization that contributes in addition to the commonly considered surface polarization. In this work a new practical implementation is described for quantitatively evaluating both volume and surface polarization contributions to the solute-solvent interaction with an irregularly shaped cavity surface. For illustration, numerical results are presented on several representative small neutral, cation, and anion solutes. The volume polarization contributions to energies and dipole moments are found to be somewhat smaller than those from surface polarization, but not negligible. The results are also used to test several charge renormalization approaches that have been previously proposed in the literature. Compared to the exact volume polarization correction, these can sometimes lead to energy corrections of the wrong sign. A previously proposed method of simulating volume polarization through an additional surface polarization generally produces corrections of the right sign and of about the right magnitude.