Many simulations of the free energy of hydration of an ion in a polar solvent are performed in truncated periodic systems in which electrostatic forces are truncated and periodic boundary conditions are used to eliminate surface effects. Simulations allow accurate calculation of the properties of the truncated Hamiltonian because there are no long-range forces present. However, in order to compare with the real universe, it is necessary to correct for the effects of both truncated potentials and periodic boundary conditions. A method of calculating the continuum dielectric properties of a truncated periodic system is derived and applied to the case of a single ion in a polar solvent. If the continuum model is accurate at distances where the effects of the truncated potentials and periodic boundary conditions are significant, then the correction will be accurate and it will include all the effects of the truncated ion-solvent and solvent-solvent potentials, as well as the effects of the periodic boundary conditions. When the simulations of Straatsma and Berendsen [J. Chem. Phys. 89, 5876 (1988)] for the Ne(aq) to Na+(aq) transformation at 298 K and 0.1 MPa are corrected in this manner, the calculations with different cutoff radii between 0.9 and 1.2 nm and different periodic cell size give the same corrected result within experimental error. Similarly, Aqvist’s [J. Phys. Chem. 98, 8253 (1994)] calculations for a different model of the Ne(aq) to Na+(aq) transformation with periodic boundary conditions and varying cutoff schemes give self-consistent results, but these results are different from his results for the same model using the surface constrained all atom solvent method. Possible reasons for this discrepancy are discussed.