We present free energy perturbation calculations on the solvation free energies of the N-methylated nucleic acid bases adenine, guanine, cytosine, thymine, and uracil. This work demonstrates the importance of using thermodynamic cycles, a careful study of convergence, and the use of both single and dual perturbation topologies. We find that the calculated solvation free energies of 9-methyladenine and 1-methylthymine are close to available experimental data. Additionally, we predict the solvation free energies for 9-methylguanine, l-methylcytosine, and 1-methyluracil. The topologies used in these perturbations can be directly applied to free energy studies of higher order nucleic acid structures.