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For measuring high-frequency properties of materials by resonant techniques, one needs to obtain the resonant characteristics of the resonator, i.e., the resonant frequency fR and the bandwidth of the resonance fB. For precise measurements, accurate and real-time determination of the resonant characteristics is required. We present a complex linear regression method, which contains only the linear square-fit algorithm, and is applicable to the complex transmission coefficient data S21(f) with arbitrary phase error. Numerical simulations and experimental data show very high accuracy and stability of this technique, when compared with the standard 3-dB method and the Lorentzian-fit method. The optimum frequency span of the measurement is found to be approximately 1.5fB, where fB is the bandwidth of the resonance.