In this paper, the resonant frequencies, quality factors and bandwidths of high Tc superconducting circular microstrip patches in the presence of a dielectric superstrate loading have been studied using Galerkin testing procedure in the Hankel transform domain. The exact Green's function of the grounded dielectric slab is used to derive an electric field integral equation for the unknown current distribution on the circular disc. Thus, surface waves, as well as space wave radiation, are included in the formulation. London's equations and the two-fluid model of Gorter and Casimir are used in the calculation of the complex surface impedance of the superconducting circular disc. Galerkin testing is used in the resolution of the electric field integral equation. Two solutions using two different basis sets to expand the unknown disk currents are developed. The first set of basis functions used is the complete set of transverse magnetic and transverse electric modes of a cylindrical cavity with magnetic side walls. The second set of basis functions used employ Chebyshev polynomials and enforce the current edge condition. The computed values for a wide range of variations of superstrate thickness and dielectric constant are compared with different theoretical and experimental values available in the open literature, showing close agreement. Results are showing that the superstrate parameters should always be kept into account in the design stage of the superconducting microstrip resonators.