The antenna element in a GPS (Global Positioning System) receiver is a source of positional errors that need to be accounted for in moderate to high precision GPS systems. These errors are due to the antenna phase and group delays. In this dissertation the phase and group delays were calculated for commonly-used circularly-polarized (CP) microstrip patch antennas. The calculation uses both simple CAD (Computer Aided Design) and cavity models as well as the full-wave electromagnetic simulators Ansoft HFSS and Ansoft Designer. Results for right-handed circularly polarized (RHCP) antennas fed in two different ways are explored: the first is an orthogonal-feed antenna and the second is a diagonal-feed antenna. Each type of antenna is designed for both non-symmetric feeding and symmetric feeding. All results are for operation at the Li frequency (1.575 GHz). It is shown that the group delay is much larger than the phase delay, due to the high-Q nature of the patch antenna (low bandwidth). Of particular interest is the variation of the phase and group delays with observation angles, since this translates into delays that will be different for each satellite signal. And hence directly corresponds to a positional error. Some signal processing results are also shown to demonstrate how the phase and group delays introduce timing errors into the GPS signal. This verifies that the phase and group delays are very important for high precision GPS and that they can be obtained directly from the various models for the GPS microstrip antennas.