Many recent observational and theoretical studies suggest globular clusters (GCs) host compact object populations large enough to play dominant roles governing their overall dynamical evolution. Yet direct detection, particularly of black holes and neutron stars, remains rare and limited to special cases, such as when these objects reside in close binaries with bright companions. Here we examine the potential of microlensing detections to further constrain these dark populations. Based on stateof-the-art GC models from the CMC Cluster Catalog, we estimate the microlensing event rates for black holes, neutron stars, white dwarfs, and, for comparison, also for M dwarfs in Milky Way GCs, as well as the effects of different initial conditions on these rates. Among compact objects, we find that white dwarfs dominate the microlensing rates, simply because they dominate by numbers. We show that microlensing detections are in general more likely in GCs with higher initial densities, especially in clusters that undergo core-collapse where the lenses are white dwarfs. We also estimate microlensing rates in the specific cases of M22 and 47 Tuc using our best-fitting models for these GCs. Because their positions on the sky lie near the rich stellar backgrounds of the Galactic bulge and the Small Magellanic Cloud, respectively, these clusters are among the Galactic GCs best-suited for dedicated microlensing surveys.