This thesis describes original work on the broadband and multiband matching of microstrip patch antennas. Microstrip patch antennas suffer from many constraints on their performance. One major restriction is their narrow impedance bandwidth. An effective method to resolve this is adding more resonators to the antenna structure to achieve multi-resonance and hence wider bandwidth. Structures such as circular, square and triangular patch antennas may support two orthogonal resonant modes or polarisations. This allows excitation of an additional resonance beside the fundamental. With the correct coupling between the resonant modes, the impedance bandwidth can be significantly increased. The equivalent circuit of such structures is similar to those used in microwave filter design. Using techniques normally employed in filter synthesis, the equivalent circuits can be generated, and aid in finding the couplings and dimensions of the specified antenna requirement. The bandwidth of circular microstrip patch antennas is significantly increased by exciting two modes on a single circular microstrip antenna, and four modes using two stacked circular microstrip patches. In this work, the designs are also extended into multimode antennas achieving multi-frequency operation.