The great majority of known muonium defect centres and muonium substituted organic radicals have essentially spin-only magnetism, with few exhibiting any noticeable departure from the free-electron g-factor. This may well be because any species with significant spin-orbit coupling would show huge g-factor anisotropy, if static, or fierce electron-spin relaxation if dynamic, broadening its transverse-field spectrum beyond detection in either case. The effects transmitted to the muon spin in longitudinal field are much milder, however, so that the usual features of repolarization, relaxation and level-crossing resonance should still be visible, and well within ISIS pulsed-source capabilities. We propose a renewed search for the diatomic SMu radical in sulphur, which would demonstrate these properties, and also in condensed carbonyl sulphide, where its yield should be greater.