We present deep infrared (2.2 mum) imaging of the Galactic microquasars 1E
1740-2942 and GRS 1758-258 using the Keck I 10 m telescope in 1998 June. Th
e observations were taken under excellent seeing conditions full width at h
alf-maximum), making them exceptionally deep for these (similar to0."45 cro
wded fields. We used the USNO-A2.0 catalog to astrometrically calibrate the
infrared images (along with an optical CCD image in the case of GRS 1758-2
58), providing independent frame ties to the known radio positions of the o
bjects. For 1E 1740-2942, we confirm potential candidates for the micro-qua
sar previously identified by et al. and show that none of the objects near
the microquasar have Marti varied significantly from 1998 to 1999. For GRS
1758-258, our astrometry indicates a position shifted from previous reports
of candidates for the microquasar. We find no candidates inside our 90% co
nfidence radius to a 2 sigma limiting magnitude of K-s = 20.3 mag. We discu
ss the implications of these results for the nature of the microquasar bina
ry systems.