In all known superconductors, the supercurrent is carried by Cooper pairs which consist of spin-1/2 quasiparticles in either spin-singlet (the usual case) or spin-triplet (the unusual case) bound states. The crystalline symmetry fixes the effective spin of the Bloch electrons and in some cases (e.g. in the presence of strong spin-orbit interactions) they can behave as spin-3/2 particles. Recently, evidence was found of unconventional superconductivity emerging from a spin-3/2 quasiparticle electronic structure in the half-Heusler semimetal YPtBi. Our planned transverse-field muon-spin rotation experiments will utilise the low-background, long time sensitivity and high statistics available on the MuSR instrument to measure the superconducting ground state in this highly unusual spin-3/2 superconductor.