Generalized Born (GB) models are widely used to study the electrostatic energetics of solute molecules including proteins. Previous work demonstrates that GB models may produce satisfactory solvation energies if accurate effective Born radii are computed for all atoms. Our previous study showed that a GB model which reproduces the solvation energy may not necessarily be suitable for ligand binding calculations. In this work, we studied binding energetics using the exact GB model, in which Born radii are computed from the Poisson-Boltzmann (PB) equation. Our results showed that accurate Born radii lead to very good agreement between GB and PB in electrostatic calculations for ligand binding. However, recently developed GB models with high Born radii accuracy, when used in large database screening, may suffer from time constraints which make accurate, large-scale Born radii calculations impractical. We therefore present a multiscale GB approach in which atoms are divided into two groups. For atoms in the first group, those few atoms which are most likely to be critical to binding electrostatics, the Born radii are computed accurately at the sacrifice of speed. We propose two alternative approaches for atoms in the second group. The Born radii of these atoms may simply be computed by a fast GB method. Alternatively, the Born radii of these atoms may be computed accurately in the free state, and then, a variational form of a fast GB method may be used to compute the change in Born radii experienced by these atoms during binding. This strategy provides an accuracy advantage while still being fast enough for use in the virtual screening of large databases.