We present a new method to estimate phase velocities of Love waves from horizontal-motion seismograms of microtremors, obtained with seismic sensors placed around two circumferences of different radii, under the assumption that the fundamental mode dominates. We applied our new method to field data acquired at a test site where the shallow underground seismic velocity profile is known, and have confirmed that the phase velocities of the fundamental-mode Love waves could be inferred with sufficient precision within certain wavelength ranges. Outside the wavelength ranges suitable for analysis, the "spectral ratio," an intermediary quantity calculated from measurement records prior to phase velocity evaluation, deviated from theoretical expectations. The pattern of deviations could satisfactorily be accounted for by considering three factors theoretically: the presence of higher-mode surface waves, directional aliasing related to the finite number of sensors, and the presence of incoherent noise.