  We demonstrate that polarimetric interferometry can be used to extract
precise spatial information about compact polarized flares of Sgr A*. We show
that, for a faint dynamical component, a single interferometric baseline
suffices to determine both its polarization and projected displacement from the
quiescent intensity centroid. A second baseline enables two-dimensional
reconstruction of the displacement, and additional baselines can self-calibrate
using the flare, enhancing synthesis imaging of the quiescent emission. We
apply this technique to simulated 1.3-mm wavelength observations of a "hot
spot" embedded in a radiatively inefficient accretion disk around Sgr A*. Our
results indicate that, even with current sensitivities, polarimetric
interferometry with the Event Horizon Telescope can achieve ~5 microarcsecond
relative astrometry of compact flaring structures near Sgr A* on timescales of
minutes.
