Differential capacitance data is one of the most widely used experimental quantities for characterizing the structure of electrolyte solutions near charged interfaces. Many studies have attempted to fit differential capacitance data to generalized Poisson-Boltzmann models, particularly to account for finite-volume, ion-crowding effects. We consider the inverse problem: the derivation of generalized Poisson-Boltzmann type free energies from prescribed differential capacitance data.