Pseudocapacitors are energy-storage devices characterized by fast and reversible redox reactions that enable them to store large amounts of electrical energy at high rates. We simulate the response of pseudocapacitive electrodes under realistic conditions to identify the factors that determine their performance, focusing on ruthenium dioxide as a prototypical electrode material. Electronic-structure methods are used together with a self-consistent continuum solvation model to build a complete database of free energies as the surface of the charged electrode is gradually covered with protons under applied voltage. The resulting database is exploited to compute hydrogen-adsorption isotherms and charge--voltage responses by means of grand-canonical sampling, finding close agreement with experimental voltammetry. These simulations reveal that small changes in the intrinsic double-layer capacitance on the order of 5 μF/cm² induce considerable variations of as much as 40 μF/cm² in the overall interfacial pseudocapacitance.