Abstract 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 three years, and we measured the brightness and positions of ∼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 six of these events, and derive mass constraints for the lens in each of them. 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, extrasolar planets, using precise ground- and space-based observations.