This document presents a method for measuring the properties of binary stars using coherently integrated visibility phases from interferometric data. The method fits the binary star model to the phase data to determine the separation, orientation, and brightness ratio as a function of wavelength. The method is demonstrated on data from the Navy Precision Optical Interferometer (NPOI) of two binary stars, θ2 Tauri and κ Ursae Majoris. For θ2 Tauri, the separation is measured to 0.16% precision, and the brightness ratio is determined with an accuracy comparable to prior work despite using less data. For κ Ursae Majoris, discrepancies in the wavelength calibration between spectrographs limited the fit quality