Orbital parameters of stellar companions can be constrained by multi-epoch observations where the astrometric position relative to the host star is measured. Additionally, radial velocity (RV) measurements of the host star may constrain the companion mass. We describe two major advances for high contrast imaging systems that significantly improve estimation of orbital parameters and masses. First, well-calibrated fiducial satellite speckles are inserted in the science images by way of deformable mirror (DM) modulation to improve astrometric measurement accuracy. Second, radial velocity measurement of the companion light reveals its velocity along the line-of-sight. We describe how the two techniques, together, can efficiently constrain orbital parameters and masses, and can do so over a shorter observation time baseline than previously possible. We demonstrate our technique with the REACH (Rigorous Exoplanetary Atmosphere Characterization with High dispersion coronagraphy) instrument at the Subaru Telescope. REACH takes extreme adaptive optics corrected light via single mode fiber from the SCExAO instrument and injects it to the high-resolution (R<70000) infrared spectrograph IRD instrument. With this technique we can achieve an astrometric precision of 1.7 mas and simultaneously measure radial velocity to a precision of <2 m/s. This high precision technique can also be extended to determine the orbits and characterize young massive planets around M-type stars.