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In this paper, a novel technique to develop multifrequency microstrip patch antennas with polarization diversity or circular polarization is presented. The proposed approach consists of exciting modes with orthogonal polarizations in microstrip patches partially filled with Composite Right/Left-Handed (CRLH) cells. Two different kinds of quad-frequency single-layer patch antennas are proposed. The first one has two orthogonal ports with high isolation between them. The second kind of quad-frequency patch antennas consists of exciting the four modes with two orthogonal polarizations through only one port. Finally, the proposed approach is used to develop dual-frequency circularly-polarized (CP) patch antennas by exciting the modes with orthogonal polarizations in quadrature phase. Prototypes of all the designs are manufactured and measured, showing good performance.