  We report on the first results from a large-scale observing campaign aiming
to use astrometric microlensing to detect and place limits on the mass of
single objects, including stellar remnants. We used the Hubble Space Telescope
to monitor stars near the Galactic Center for 3 years, and we measured the
brightness and positions of $\sim$2 million stars at each observing epoch. In
addition to this, we monitored the same pointings using the VIMOS imager on the
Very Large Telescope. The stars we monitored include several bright
microlensing events observed from the ground by the OGLE collaboration. In this
paper, we present the analysis of our photometric and astrometric measurements
for 6 of these events, and derive mass constraints for the lens in each of
these. Although these constraints are limited by the photometric precision of
ground-based data, and our ability to determine the lens distance, we were able
to constrain the size of the Einstein ring radius thanks to our precise
astrometric measurements, the first routine measurements of this type from a
large-scale observing program. This demonstrates the power of astrometric
microlensing as a tool to constrain the masses of stars, stellar remnants, and,
in the future, of extrasolar planets, using precise ground- and space-based
observations.
