We study lambda-integration paths, specifically designed for calculating "exact" surface and interfacial free energies of solids at elevated temperatures using molecular dynamics or Monte Carlo simulation methods. We compare various paths with the standard technique of thermodynamic integration by application to the surface free energy for the (100) and (110) faces of alpha iron using embedded atom method (EAM) potentials. We demonstrate which paths are completely reversible at high temperatures and show consistency of results for these paths. The lambda-integration paths can be applied with confidence to find equilibrium surface free energies, within the limits of the surface area, intermolecular potentials and other approximations implicit to the simulation methods used.