  We introduce a new method of searching for and characterizing extra-solar
planets. We show that by monitoring the center-of-light motion of microlensing
alerts using the next generation of high precision astrometric instruments the
probability of detecting a planet orbiting the lens is high. We show that
adding astrometric information to the photometric microlensing lightcurve
greatly helps in determining the planetary mass and semi-major axis. We
introduce astrometric maps as a new way for calculating astrometric motion and
planet detection probabilities. Finite source effects are important for low
mass planets, but even Earth mass planets can give detectable signals.
