The measurement of Higgs couplings constitutes an important part of present standard model precision tests at colliders. We show that modifications of Higgs couplings induce energy-growing effects in specific amplitudes involving longitudinally polarized vector bosons, and we initiate a novel program to study these effects off shell and at high energy, rather than on the Higgs resonance. Our analysis suggests that these channels are complementary and competitive with familiar on-shell measurements; moreover, they offer endless opportunities for refinement and improvements.