The use of electrostatic cutoffs in calculations of free energy changes by molecular dynamics or Monte Carlo simulation is known to introduce errors, which can be quite large when the net charge of the system is changed. The Born equation has often been used to correct for such errors, but this and other analytical methods cannot be used for many systems with complicated structures. Here, we show that numerical methods for solving the Poisson equation, which have been extensively developed recently for studies of solvation thermodynamics, provide a more generally applicable alternative to the traditional Born-type corrections.