We studied the hydration and the first hydrolysis reaction of U(IV) and Np(IV) ions in an aqueous environment, applying a relativistic density functional method together with a recently proposed variant of a continuum solvation model where the solute cavities are constructed with effective atomic radii, based on charge-dependent scaling factors. In this way, one obtains improved solvation energies of charged species. We demonstrate that solute cavities, constructed with scaled atomic radii as described, permit one to calculate hydrolysis constants of acceptable accuracy. As a consequence, one is also able to estimate free hydration energies of U(IV) and Np(IV) in adequate agreement with empirical data. According to the model calculations, U(IV) is coordinated by eight to nine water molecules, while the preferred coordination number of Np(IV) is 8. For the highly charged ions under study, the modified solvation model simultaneously yields improved geometries, hydration energies, and hydrolysis constants.