Radial velocity monitoring has revealed the presence of moving broad emission lines in some quasars, potentially indicating the presence of a sub-parsec binary system. Phase-referenced, near-infrared interferometric observations could map out the binary orbit by measuring the photocenter difference between a broad emission line and the hot dust continuum. We show that astrometric data over several years may be able to detect proper motions and accelerations, confirming the presence of a binary and constraining system parameters. The brightness, redshifts, and astrometric sizes of current candidates are well matched to the capabilities of the upgraded VLTI/GRAVITY+ instrument, and we identify a first sample of 10 possible candidates. The astrometric signature depends on the morphology and evolution of hot dust emission in supermassive black hole binary systems. Measurements of the photocenter offset may reveal binary motion whether the hot dust emission region is fixed to the inner edge of the circumbinary disk, or moves in response to the changing irradiation pattern from an accreting secondary black hole.