Convective heating is a traditional method used for the drying of wet porous materials. Currently, microwave drying has been employed for this purpose, due to its excellent characteristics of uniform moisture removal and heating inside the material, higher drying rate, and low energy demand. This paper focuses on the study of the combined convective and microwave drying of porous solids with prolate spheroidal shape. An advanced mathematical modeling based on the diffusion theory (mass and energy conservation equations) written in prolate spheroidal coordinates was derived and the numerical solution using the finite-volume method is presented. Here, we evaluated the effect of the heat and mass transport coefficients and microwave power intensity on the moisture removal and heating of the solid. Results of the drying and heating kinetics and the moisture and temperature distribution inside the solid are presented and discussed. It was verified that the higher the convective heat and mass transfer coefficients and microwave power intensity, the faster the solid will dry and heat up.