In this article, we present two efficient closed-form models to examine thoroughly the dependence of resonant frequency, quality factor, probe reactance, input impedance, bandwidth, and gain on parameters such as patch radius, probe location, substrate electrical parameters, and air gap of a coax probe-fed circular patch antenna. The implementation of these models is very easy and the computation cost is very low. The proposed models show excellent agreements with experimental and simulation results. We have also investigated experimentally the gain patterns of a suspended substrate circular patch antenna.