Several experiments search for μ ↔ e flavour change, for instance in μ → e conversion, μ → eγ and μ → eēe. This paper studies how to translate these experimental constraints from low energy to a New Physics scale M m W . A basis of QCD × QED-invariant operators (as appropriate below m W ) is reviewed, then run to m W with one-loop Renormalisation Group Equations (RGEs) of QCD and QED. At m W , these operators are matched onto SU(2)-invariant dimension-six operators, which can continue to run up with electroweak RGEs. As an example, the μ → eγ bound is translated to the scale M, where it constrains two sums of operators. The constraints differ from those obtained in previous EFT analyses of μ → eγ , but they reproduce the expected bounds on flavour-changing interactions of the Z and the Higgs, because the matching at m W is pragmatically performed to the loop order required to get the "leading" contribution.