The influence of a ferromagnetic substrate on microwave surface resistance of high-temperature superconductors is numerically studied through finite element method computations. For a superconductor with a ferromagnetic substrate underneath, it is observed that an increase in ferromagnet susceptibility results in more shielding of the superconductor from the influence of external magnetic field and, in turn, a fall in microwave surface resistance. The effect saturates with higher susceptibilities where a plateau is reached in the surface resistance curve. As a comparison, coating superconductor with U-shaped ferromagnets on two sides is also considered where an ordinary hysteresis curve in terms of microwave surface resistance is observed for a non-magnetic coating. In contrast, a highly ferromagnetic coating with a relative permeability of 1000 gives rise to an unusual hysteresis behavior.