Accurate astrometry is crucial for determining orbits of near-Earth-asteroids (NEAs) and therefore better tracking them. This paper reports on a demonstration of 10 milliarcsecond-level astrometric precision on a dozen NEAs using the Pomona College 40 inch telescope, at the JPLs Table Mountain Facility. We used the technique of synthetic tracking, in which many short exposure (1 second) images are acquired and then combined in post-processing to track both target asteroid and reference stars across the field of view. This technique avoids the trailing loss and keeps the jitter effects from atmosphere and telescope pointing common between the asteroid and reference stars, resulting in higher astrometric precision than the 100 mas level astrometry from traditional approach of using long exposure images. Treating our synthetic tracking of near-Earth asteroids as a proxy for observations of future spacecraft while they are downlinking data via their high rate optical communication laser beams, our approach shows precision plane-of-sky measurements can be obtained by the optical ground terminals for navigation. We also discuss how future data releases from the Gaia mission can improve our results.