In this paper, a theoretical modeling of the microstrip patch antenna parameters is presented. The modeling considers some of the main goals of antenna design such as antenna impedance, losses, gain, radiation efficiency, and return loss. The modeling follows the progression of relating the aforementioned goals to the dissipation factor of the substrate material. The progression in modeling lays out the equations, methodically, to show how the dissipation factor affects the design goals. The modeling is backed by simulations and measurements results. The novelty lies in picking the new Rogers Kappa-438 substrate (which is identical to the FR4), to greatly improve the microstrip patch antenna performance. The results obtained and displayed, are for the input impedance, gain, return loss and the radiation pattern. A comparison in performance between the new Rogers Kappa-438 substrate results and the FR4 substrate results is made. The comparison is based on both simulations results and measurements results. In order to make the comparison, two circular microstrip patch antennas were designed and fabricated at the 1.8GHz cellular band; one is based on the FR4 substrate; the other is based on the Kappa-438 substrate. Comparisons between the Kappa-438 performance with results published in the literature based on the overall size, return loss, and gain are also made. The measured gain and radiation pattern were taken for a single frequency, while the input impedance and return loss were measured across the frequency band dictated by the limits of the measurement device.