The Range Limited Antenna (RLA) is a device, which accurately estimates the range of incoming signals and rejects those that arrive from outside a certain, pre-determined range. This task is accomplished by using two multi-element arrays and applying direction finding (DF) algorithms on each of them. Rectangular, single-layer, coax-fed patch antennas are used as array elements for the specific purpose of tracking cell phones operating in the PCS band inside a given building. It is vital to ensure that the patch antenna is designed in such a manner that it resonates at the desired frequency. This thesis introduces the Agilent High Frequency Structure Simulator (HFSS) as an effective tool for modeling electromagnetic structures. It presents a comprehensive and meticulous description of the process of modeling a rectangular coax-fed patch antenna in HFSS. Plots of S-parameter values are calculated and are compared with WIPL-D, which is another simulation software program, and with measurements performed at the George Washington University. Various important parameters of the HFSS simulation are varied and their effects are investigated to provide a deeper understanding of the program. / Master of Science