Wavefront sensors that can operate at low light levels, be built from present technology components, and provide accurate wavefront phase estimates in real time are required for use with adaptive optics systems. The use of estimation theory makes possible the evaluation of wavefront sensors without specification of the wavefront phase estimation algorithms. The Cramer-Rao method was used to find a lower bound on integrated rms wavefront sensor estimation error. In addition to an analysis of the general case, the error lower bound was numerically evaluated for the shearing interferometer wavefront sensor. Computer simulations of the atmosphere and wavefront sensor measurements including noise were performed. Using an appropriate algorithm, the phase was estimated and the resulting phase error was compared with the lower bound. The results support the validity of using the Cramer-Rao lower bound to evaluate wavefront sensor performance.