We study the production of sterile neutrinos in supernovae, focusing in particular on the keV-MeV mass range, which is the most interesting range if sterile neutrinos are to account for the dark matter in the Universe. Focusing on the simplest scenario in which sterile neutrinos mixes only with muon or tau neutrino, we argue that the production of keV-MeV sterile neutrinos can be strongly enhanced by a Mikheyev-Smirnov-Wolfenstein (MSW) resonance, so that a substantial flux is expected to emerge from a supernova, even if vacuum mixing angles between active and sterile neutrinos are tiny. Using energetics arguments, this yields limits on the sterile neutrino parameter space that reach down to mixing angles on the order of sin 2 2θ 10 −14 and are up to an order of magnitude stronger than those from X-ray observations. While supernova limits suffer from larger systematic uncertainties than X-ray limits they apply also to scenarios in which sterile neutrinos are not abundantly produced in the early Universe. We also compute the flux of O(MeV) photons expected from the decay of sterile neutrinos produced in supernovae, but find that it is beyond current observational reach even for a nearby supernova.1 In this work, for brevity, the term "sterile neutrino" is denoting both sterile neutrinos and antineutrinos. The only exception is when discussing the adiabatic production where we refer explicitly to "sterile antineutrinos" because the resonance appears in the antineutrino channel.