Methods and intermolecular potentials apt for the molecular simulation of solubilities of solids in supercritical fluids are briefly reviewed. As an illustrative example, the solubilities of naphthalene in supercritical carbon dioxide at 328.15 K are studied using an isotropic multipolar potential model. Upon using the Widom insertion method, a quantitative prediction of the experimental data is obtained. A further look at the calculations shows that the customary implementation of the method is tainted by the use of experimental information about the vapor pressure and density of the solid. If the actual properties (obtained via simulation) of the model solid are used, the equilibrium is, in this example, poorly described. Full-scale molecular dynamic simulations, which include both the solid and fluid phases, confirm the results. It is shown how an accurate description and modeling of the solute solid-phase properties is a prerequisite for the determination of the solubilities of solids in supercritical fluids.