What is the scale of new physics behind the muon g-2?

We study the constraints imposed by perturbative unitarity on the new physics interpretation of the muon anomaly. Within a Standard Model effective field theory approach, we find that scattering amplitudes sourced by effective operators saturate perturbative unitarity at about 1 PeV. This corresponds to the highest energy scale that needs to be probed in order to resolve the new physics origin of the muon anomaly. On the other hand, simplified models (e.g., scalar-fermion Yukawa theories) in which renormalizable couplings are pushed to the boundary of perturbativity still imply new on-shell states below 200 TeV. We finally suggest that the highest new physics scale responsible for the anomalous effect can be reached in nonrenormalizable models at the PeV scale.