The electrostatic contribution to the solvation free energy of the 20 naturally occurring amino acids is examined using atomic models. The amino acids are modeled by N-acetyl-X-N’-methylamide. Free energy perturbation techniques with explicit water molecules are used to evaluate the contribution of solute-solvent electrostatic interactions to the solvation flee energies. An analysis based on the radial solvent charge distribution yields a basic rule to determine a set of atomic Born radii defining the dielectric boundary between the solute and the solvent in continuum electrostatic models. Minor adjustments are made to refine the atomic Born radii in order to reproduce quantitatively the electrostatic contribution to the solvation free energy calculated by free energy perturbation techniques. The good agreement of continuum electrostatic and molecular dynamics free energy perturbations suggests that the new set of atomic Born radii may be used as a computationally inexpensive alternative to the microscopic treatment of solvent with explicit water molecules.