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We have combined new infrared radial velocities and previously obtained spectropolarimetric observations to compute orbits of the M6 giants in two southern S-type symbiotic systems. The spectropolarimetric data enable the orbital inclinations of the systems to be determined, placing greater constraints on the properties of the components. V455 Sco has a circular orbit with a period of 1398 ± 6 days and an inclination of 94° ± 1°. The orbit of SS 73-90 has a period of 898 ± 5 days, a modest eccentricity of 0.16, and an inclination of 97° ± 7°. The center of mass velocity of each system is large, −77.9 km s−1 for V455 Sco and 89.5 km s−1 for SS 73-90, making them members of the old disk population. The M giant component of each system is likely on the asymptotic giant branch. From estimates of the M giants' radii we predict that both systems are eclipsing and provide ephemerides to search for the eclipses. For V455 Sco, the predicted eclipses are found in data from the Harvard College Observatory plate archives. The He ii emission feature near 1.0123 μm is associated with the hot component in both systems. However, the orbits produced from the emission-line radial velocities do not lead to masses that are consistent with other results.