Direct-potential-fit analyses of the ground X1Σ+X1Σ+ electronic states of NeH+ and ArH+ are carried out. The analyses provided accurate potential energy functions for NeH+ and ArH+. Radial functions describing Born-Oppenheimer breakdown effects are furnished for both cations. Comparisons of the fitted potential energy functions are made with reliable ab initio functions. The model for the potential energy includes a full account of the known long-range behavior.