The conventional Wheeler cap method usually produces accurate radiation efficiency of small antennas when the antennas under test (AUTs) operate as a simple series or a parallel RLC resonance circuit. However, this method often gives unreliable radiation efficiency if the AUT has a complicated operating principle such as circular polarization (CP), multiple resonances, or broad-band properties. In this paper, we propose an improved Wheeler cap method based on the equivalent high-order circuit model including transformers to provide accurate radiation efficiency, although the AUT does not operate as a simple resonance circuit. For building equivalent high-order circuit models, a method for estimating the initial values of a genetic algorithm (GA) is also proposed, which effectively reduces the searching space and improves the convergence of the optimization. To verify the proposed method, we measure the radiation efficiency of a CP microstrip antenna, a UHF RFID tag antenna, and a triple-resonance microstrip antenna.