The recent application of numerical Poisson-Boltzmann methods to the determination of the electrostatic potential and counterion distributions around polyelectrolytes such as DNA has prompted the determination of accurate solvent dielectric constants. The previous assumption for proteins of using a constant value of about 80 for the solvating environment appears inadequate when dealing with the much higher potential gradients and local ion concentrations of charged polyelectrolytes in solution. Approximations using lower dielectric values near 30 at the surface and increasing away to a bulk value of 78.5 have been incorporated into modem finite-difference Poisson-Boltzmann techniques and have led to more reasonable estimates of counterion distributions. However, choosing this dielectric constant "field" has been more a matter of guessing than scientific analysis. To put these techniques on a firmer foundation, we present a simple calculational procedure for determining dielectric constants near the surface of macromolecules and lipid membranes. To demonstrate the soundness of the calculation we compare calculated dielectric constants near the surface of DNA with data from recent experiments measuring this quantity in both the major and minor grooves of B-form DNA. This procedure can be useful for proteins as well and may be particularly applicable in solvent pockets where strong potential gradients lead to the electrostatic guiding of ions or ligands toward specific binding sites.