The dielectric constants of myoglobin, apomyoglobin, the B fragment of staphylococcal protein A, and the immunoglobulin-binding domain of streptococcal protein G are calculated from 1-2 ns molecular dynamics simulations in water, using the Frohlich-Kirkwood theory of dielectrics. This dielectric constant is a direct measure of the polarizability of the protein medium and is the appropriate macroscopic quantity to measure its relaxation properties in response to a charged perturbation, such as electron transfer, photoexcitation, or ion binding. In each case the dielectric constant is low (2-3) in the protein interior, then rises to 11-21 for the whole molecule. The large overall dielectric constant is almost entirely due to the charged protein side chains, located at the protein surface, which have significant flexibility. If these are viewed instead as part of the outer solvent medium, then the remainder of the protein has a low dielectric constant of 3-6 (depending on the protein), comparable to that of dry protein powders. Similar results were already observed for ferro- and ferricytochrome c, and are probably valid for many or most stable globular proteins in solution, leading to a rather comprehensive picture of charge screening and the dielectric constant of proteins. This picture suggests ways, and supports some ongoing efforts, to improve current Poisson-Boltzmann models. Indeed, treating a protein as a homogeneous, low dielectric medium is likely to underestimate the actual dielectric relaxation of the protein; this would affect calculations of the self-energy of titrating protons, or the reorganization energy of a redox electron.