The calculation of binding free energies between highly charged species is a major challenge for free energy simulations. In this study, we applied a combination of molecular dynamics simulations and continuum electrostatics, along with normal-mode analysis, to compute the absolute free energies of binding between cobalt (III) hexammine and two RNA fragments for which NMR structures have been determined. The predicted affinities, using the finite-difference Poisson-Boltzmann method with a solute dielectric constant of I to treat solvation, were overall underestimated relative to the experimental values. However, internal consistency in the calculated energies was maintained between the different trajectories, and the structures in the simulations gave excellent agreement with NMR data. Various models for obtaining the electrostatic contributions were analyzed, including the effects of solute dielectric constants and van der Waals radii, linear and nonlinear salt contributions, as well as results from generalized Born versus finite-difference Poisson-Boltzmann models. These provide insight into the strengths and limitations in the current methods and force fields for free energy calculations.