Anomalous Higgs couplings precipitate unitarity violation in a multitude of processes. These include, in particular, high multiplicity (2 → more than 2) processes involving longitudinal vectors, where unitarity violation manifests in cross-sections that grow too quickly with energy. Using EFT―which provides a transparent and systematic parameterization of the energy growth―we explore how to exploit this energy growth to measure/constrain anomalous Higgs couplings. In certain (important) channels, these high-energy probes turn out to be both complementary and competitive with standard on-shell measurements. Additionally, our exploratory analysis contains many exciting avenues for refinements and improvements for both theorists and experimentalists.