The simplicity and intuitive design of traditional circularly polarized (CP) patch antennas, such as the truncated corner patch antenna, has led to their widespread popularity. However, they are limited to a narrowband performance on the order of 0.1%-2% for simultaneously good and axial ratio (AR). We will prove theoretically that this is a direct result of the probe reactance hindering the use of thicker substrates to increase the bandwidth. Furthermore, we propose a novel compensation technique to enhance the bandwidth capabilities of these CP patch antennas. Our method inserts a capacitive element, such as an annular gap or parallel plate, in series with the probe inductance to remove its effect. We demonstrate this technique with simulations and measurements to obtain AR-bandwidth capabilities as high as 12.6%. To the authors' best knowledge, this is the first time that capacitive compensation and thick substrates have been jointly employed to enable broadband CP patch antennas.