Symbiotic stars are interacting binaries consisting of a giant star transferring mass onto a hot, compact companion — typically, a white dwarf. The Sloan Digital Sky Survey-IV Apache Point Observatory Galactic Evolution Experiment (APOGEE) Data Release 16 (DR16) provides high-resolution (R ~ 22,500), multi-epoch, infrared (1.51 to 1.69 micron) spectra of the red giant-component (the hot, compact component is not detectable at these wavelengths) for three such systems contained in two of the Local Group dwarf galaxies. These systems — LIN 445a (SMC N73) and LIN 358 in the Small Magellanic Cloud, and Draco C1 in the Draco dwarf spheroidal — have a sufficient number of precise radial velocity measurements in DR16 for the fitting of orbital parameters for the binary. We report improved mass measurements for each component in each system as derived from the precise stellar parameters from APOGEE (effective temperature and surface gravity) for the giant and the derived orbital elements. By constraining the geometries of these binaries, this work aims to assess possible accretion mechanisms fueling these symbiotic stars.