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Summary form only given. We present the formulation of the moment method applied to the determination of phase profiles of microwave beams from known amplitudes. Although used in optics, this numerical method has never before been applied to the phase retrieval of a microwave beam. While traditional approaches to this problem employ an iterative error-reduction algorithm, the moment method calculates an initial two-dimensional polynomial phasefront based on weighted moments of intensity measurements. Since this novel formulation calculates the moments of quasi-optical Gaussian-like beams, the moment method has the very important advantage of quantifying and compensating for measurement error. A brief introduction of the theory behind the moment method is presented. The validity of the moment method is confirmed by examining a simple case of an ideal Gaussian beam. A manufactured example to measurement error is then introduced to highlight the advantages of retrieving the phase using the moment method. The effectiveness of the approach is further demonstrated by applying intensity measurement from cold-test gyrotron data to calculate a phasefront solution via the moment method. The accuracy of these results is shown to be comparable with that obtained from the previously developed iteration method. Future developments for the moment method are discussed.