Magnetic skyrmions are topologically protected objects that exist in the spin texture of certain magnetic materials. We have shown that muon spin relaxation is a powerful technique for studying the physics of skyrmions and related magnetic textures. Here we propose to extend our investigations of skyrmions to two new recently observed skyrmionic states of matter that are topologically distinct from conventional skyrmions, biskyrmions in NiMnGa, and antiskyrmions in the Heusler alloy Mn1.4Pt0.9Pd0.1Sn. This work will enable a broader understanding of the dynamics of skyrmionic spin textures and help push the field closer to practical applications in spintronics devices.