A computational approach for resonant frequencies of cylindrical substrate-mounted resonators is presented in this paper. The resonator is made of ferrite material, which is magnetically anisotropic and characterized by a Hermitian tensor. It is mounted on top of a grounded dielectric substrate, and the entire assembly is covered with a tuning plate, leaving the sidewalls open. The generalized impedance boundary conditions (GIBCs) are derived for the ferrite material and are used to formulate the approximate solution to the boundary-value problem. The resulting transcendental equations are solved numerically, and variations of the resonant frequency with respect to bias field, magnetization, and dimensions of the structure are reported.