The electron spin resonance spectra of VC, VSi, NbC, and NbSi trapped in the solid rare gases (Ne, Ar, Kr) show, principally through the large negative values of DELTA-g parallel-to = g parallel-to - g(e), that the orbital angular moments of these molecules in their (proposed) ground 2-DELTA states are partially quenched. Observed metal hyperfine splittings also vary with the matrix gas. This unprecedented effect in rare-gas matrices is attributed to strong unsymmetrical interaction of these ionic molecules with the matrix such that each is situated in an orthorhombic crystal field. The crystal-field-splitting parameter delta is both molecule and matrix dependent, varying from approximately 1400 to 7800 cm-1.