Motivated by the existence of binary systems where a stellar-mass black hole is bound to a normal star, we selected four red giants with large radial velocity (RV) variation from the survey of Space Interferometry Mission (SIM) grid stars and monitored their RVs for several months. None turned out to contain a massive companion above 2.5 solar masses. The red giant TYC 9299-1080-1 with a large RV and a large proper motion is a single-lined spectroscopic binary with a period of 81 days. It is an extreme halo object moving at 350 km/s almost directly toward the Galactic center. HD 206092 is a double-lined binary with a short period of 4.37 days. It belongs to the rare class of active RS CVn-type binaries with evolved primary components, apparently undergoing mass transfer. The X-ray luminosity of HD 206092 is about twice as high as the most luminous coronal X-ray emitters observed by ROSAT, including II Peg and the prototype star RS CVn. HD 318347 has a variable double-peaked emission-line spectrum (not a giant), while HD 324668 has a constant RV. Despite the overall good quality of the SIM survey data confirmed by a comparison with Gaia Data Release 2 (DR2, Cat. I/345) mean RVs, the few large RV variations are explained, mostly, by erroneous data. We discuss the significance of the non-detection of massive companions in the SIM grid sample and the associated work.