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We propose a modified Wheeler cap method to accurately measure the radiation efficiency of patch antennas with multiple resonances by modeling their impedance as a high-order circuit model. The radiation efficiency is obtained from the power consumption ratio between the radiation and loss conductances using a circuit model we developed. Our technique is validated by measuring the efficiencies of a circularly polarized microstrip patch antenna and a triple-band microstrip patch antenna. The measurement results are in close agreement with those produced by simulations, whereas the Wheeler cap method with a series-(or parallel-) resonant circuit model is shown to be unreliable.