This paper discusses approximate statistical estimates of limiting errors associated with single differential phase measurement of a time delay (phase difference) between two reflectors of the passive surface acoustic wave (SAW) sensor. The remote wireless measurement is provided at the ideal coherent receiver using the maximum likelihood function approach. Approximate estimates of the mean error, mean square error, estimate variance, and Cramér-Rao bound are derived along with the error probability to exceed a threshold in a wide range of signal-to-noise ratio (SNR) values. The von Mises/Tikhonov distribution is used as an approximation for the phase difference and differential phase diversity. Simulation of the random phase difference and limiting errors also is applied.