Though stellar-mass black holes (BHs) are likely abundant in the Milky Way (N=10^8-10^9), only ~20 have been detected to date, all in accreting binary systems (Casares 2006). Gravitational microlensing is a proposed technique to search for isolated BHs, which to date have not been detected. Two microlensing events, MACHO-1996-BLG-5 (M96-B5) and MACHO-1998-BLG-6 (M98-B6), initially observed near the lens-source minimum angular separation in 1996 and 1998, respectively, have long Einstein crossing times (>300 days), identifying the lenses as candidate black holes. Twenty years have elapsed since the time of lens-source closest approach for each of these events, indicating that if the lens and source are both luminous, and if their relative proper motion is sufficiently large, the two components should be spatially resolvable. We attempt to eliminate the possibility of a stellar lens for these events by: (1) using Keck near-infrared adaptive optics images to search for a potentially now-resolved, luminous lens; and (2) examining multi-band photometry of the source to search for flux contributions from a potentially unresolved, luminous lens. We combine detection limits from NIRC2 images with light curve data to eliminate all non-BH lenses for relative lens-source proper motions above 0.81 mas/yr for M96-B5 and 2.48 mas/yr for M98-B6. Further, we use WFPC2 broadband images to eliminate the possibility of stellar lenses at any proper motion. We present the narrow range of non-BH possibilities allowed by our varied analyses. Finally, we suggest future observations that would constrain the remaining parameter space with the methods developed in this work.