Starshades, large occulters positioned tens of thousands of kilometers in front of space telescopes, offer one of the few paths to imaging and characterizing Earth-like extrasolar planets. However, for a starshade to generate a sufficiently dark shadow on the telescope, the two must be coaligned to just 1 meter laterally, even at these large separations. The principal challenge to achieving this level of control is in determining the position of the starshade with respect to the space telescope. In this paper, we present numerical simulations and laboratory results demonstrating that a Zernike wavefront sensor coupled to a WFIRST-type telescope is able to deliver the stationkeeping precision required, by measuring light outside of the science wavelengths. The sensor can determine the starshade lateral position to centimeter level in seconds of open shutter time for stars brighter than eighth magnitude, with a capture range of 10 meters. We discuss the potential for fast (ms) tip/tilt pointing control at the milli-arcsecond level by illuminating the sensor with a laser mounted on the starshade. Finally, we present early laboratory results.