Star trackers based on the use of charge-coupled device (CCD) imaging arrays have demonstrated substantial performance gains relative to more conventional designs. For many space applications, the most important gain is the accuracy improvement associated with a stable, precisely known, CCD geometry. This inherent accuracy can be fully exploited using star image centerfinding techniques to measure the image location to a small fraction of a CCD picture element. In this paper we present the results of an extensive series of laboratory tests aimed at exploring the accuracy limits of this technique. Simulated star images were moved over the CCD, permitting measurement of tracking errors as small as 1/1000 pixel. After tests on both frontside and backside illuminated (thinned) CCDs, we conclude that tracking accuracy better than 1/50 pixel can be achieved.