Physics beyond the Standard Model can manifest itself as both new light states and heavy degrees of freedom. In this paper, we assume that the former comprise only a sterile neutrino, N . Therefore, the most agnostic description of the new physics is given by an effective field theory built upon the Standard Model fields as well as N . We show that Higgs phenomenology provides a sensitive and potentially crucial tool to constrain effective gauge interactions of sterile neutrinos, not yet probed by current experiments. In parallel, this motivates a range of new Higgs decay channels with clean signatures as candidates for the next LHC runs, including h → γ + p miss T and h → γγ + p miss T .