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Gravitational lensing provides a means to measure mass that does not rely on detecting and analysing light from the lens itself. Compact objects are ideal gravitational lenses, because they have relatively large masses and are dim. In this paper we describe the prospects for predicting lensing events generated by the local population of compact objects, consisting of 250 neutron stars, 5 black holes, and approximately 35,000 white dwarfs. By focusing on a population of nearby compact objects with measured proper motions and known distances from us, we can measure their masses by studying the characteristics of any lensing event they generate. Here we concentrate on shifts in the position of a background source due to lensing by a foreground compact object. With HST, JWST, and Gaia, measurable centroid shifts caused by lensing are relatively frequent occurrences. We find that 30-50 detectable events per decade are expected for white dwarfs. Because relatively few neutron stars and black holes have measured distances and proper motions, it is more difficult to compute realistic rates for them. However, we show that at least one isolated neutron star has likely produced detectable events during the past several decades. This work is particularly relevant to the upcoming data releases by the Gaia mission and also to data that will be collected by JWST. Monitoring predicted microlensing events will not only help to determine the masses of compact objects, but will also potentially discover dim companions to these stellar remnants, including orbiting exoplanets., 16 pages, 10 figures, 8 tables