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We present deep infrared ($2.2 \mu$m) imaging of the Galactic microquasars1E1740-2942 and GRS 1758-258 using the Keck-I 10-meter telescope in June 1998.The observations were taken under excellent seeing conditions ($\sim 0.45\arcsec$ full-width half-maximum), making them exceptionally deep for thesecrowded fields. We used the USNO-A2.0 catalog to astrometrically calibrate theinfrared images (along with an optical CCD image in the case of GRS 1758-258),providing independent frame ties to the known radio positions of the objects.For 1E1740-2942, we confirm potential candidates for the microquasar previouslyidentified by Marti et al., and show that none of the objects near themicroquasar have varied significantly from 1998 to 1999. For GRS 1758-258, ourastrometry indicates a position shifted from previous reports of candidates forthe microquasar. We find no candidates inside our 90% confidence radius to a $2\sigma$ limiting magnitude of $K_s = 20.3$ mag. We discuss the implications ofthese results for the nature of the microquasar binary systems.Comment: To appear in the Astrophysical Journal; 15 pages, including 4 figure

Deep Infrared Imaging of the Microquasars 1E 1740−2942 and GRS 1758−258