With sub-microarcsecond astrometry, exoplanets can be identified and their masses measured. Coronagraphic imaging of these exoplanets is required to study their atmospheres and surfaces in sufficient detail to identify possible signs of biological activity. We show how both measurements can be simultaneously acquired with a single telescope in which the central field is directed to a coronagraph instrument providing high contrast images, while the surrounding field is imaged with a wide field camera in which numerous faint background stars are used as an astrometric reference. To calibrate astrometric distortions due to optics and focal plane detector array imperfections and variations, we propose to place small dark spots on the telescope primary mirror. The spots, arranged in a regular grid containing no low spatial frequencies, do not affect the coronagraph performance. In the wide field image, they create diffraction spikes originating from the central bright star, which are affected by changes in intrumental distortions in exactly the same way as the background stars used for reference, thus allowing calibration of instrumental errors to micro-arcsecond level. We show that combining simultaneous astrometric and coronagraphic measurements allows reliable detection and characterization of exoplanets. Recent laboratory tests performed at the University of Arizona and NASA Ames validate the concept, demonstrating both the ability to accurately calibrate astrometric distortions, and compatibility with high contrast imaging systems.