  The long-standing muon g-2 anomaly can be explained by heavy new physics
particles through chirally enhanced contributions. It has been recently
proposed that a muon collider running at center-of-mass energies of several TeV
could test these new physics scenarios in a model-independent way, through the
study of high-energy processes such as mu+ mu- --> h gamma. In this work, we
validate these findings, based on effective field theories, by considering
selected renormalizable simplified models and by computing this one-loop
process in full generality. Furthermore, we explore the interplay of direct and
indirect high-energy searches to pin down the details of the underlying new
physics model accommodating the muon g-2 anomaly.
