The paper investigates the effects of the thickness of high-temperature superconducting (HTS) rectangular microstrip patches on resonant frequency and bandwidth. Using Galerkin's method and the two fluids model for surface impedance, the study presents numerical results, highlighting the superior performance of HTS materials in microwave technology applications. It concludes that the resonant characteristics align well with previous analytical models, demonstrating the potential benefits of utilizing HTS materials in integrated circuits and antennas.