The accuracy of continuum electrostatic models, in which the solvent is represent as a featureless dielectric medium, depends sensitively on the choice of the atomic radii used for setting the dielectric boundary between the solute and the solvent. Here, a set of optimal atomic radii for performing accurate continuum electrostatic calculations on naturally occurring nucleic acids is parametrized using molecular dynamics simulations and free energy perturbation calculations with explicit water molecules. Small model compounds constituting the building blocks of nucleic acids (base, sugar, phosphate) as well as combinations of these units (nucleoside, diphosphate sugar) are chosen to get proper representation of all the molecular moieties found in nucleic acids. Different conformations of the model compounds representative of both A-form and B-form conformations of DNA are considered. An initial set of atomic radii is first determined using a statistical mechanical analysis based on the average radial solvent charge density calculated from molecular dynamics simulations with explicit water molecules. Minor adjustments are then made to refine the radii to reproduce quantitatively the electrostatic contribution to the solvation free energy calculated by free energy perturbation techniques. The ability of the continuum dielectric approximation to accurately represent the free energy associated with base pairing is also considered by examining all possible normal and mismatched base pairs. In all cases, the agreement between molecular dynamics free energy perturbations with explicit water molecules and the continuum electrostatic calculations with optimized atomic radii is excellent. As a final illustration, the free energy profile is calculated for AT and GC base pairs as a function of base pair separation. Continuum electrostatic calculations with the optimized atomic radii provides a computationally inexpensive approach to study nucleic acids and their complexes with proteins.