A NMR protocol is introduced that permits accurate measurement of minute, remote chemical shift perturbations (CSPs), caused by a mutation-induced change in the electric field. Using protein GB3 as a model system, H-1(N) CSPs in K19A and K19E mutants can be fitted to small changes in the electric field at distal sites in the protein using the Buckingham equation, yielding an apparent dielectric constant epsilon(a) of 8.6 +/- 0.8 at 298 K. These CSPs, and their derived epsilon(a) value, scale strongly with temperature. For example, CSPs at 313 K are about similar to 30% smaller than those at 278 K, corresponding to an effective epsilon(a) value of about 7.3 at 278 K and 10.5 at 313 K. Molecular dynamics simulations in explicit solvent indicate that solvent water makes a significant contribution to epsilon(a).