We propose a resonant electromagnetic detector to search for hidden-photon dark matter over an extensive range of masses. Hidden-photon dark matter can be described as a weakly coupled "hidden electric field," oscillating at a frequency fixed by the mass, and able to penetrate any shielding. At low frequencies (compared to the inverse size of the shielding), we find that observable effect of the hidden photon inside any shielding is a real, oscillating magnetic field. We outline experimental setups designed to search for hidden-photon dark matter, using a tunable, resonant LC circuit designed to couple to this magnetic field. Our "straw man" setups take into consideration resonator design, readout architecture and noise estimates. At high frequencies,there is an upper limit to the useful size of a single resonator set by 1/\nu. However, many resonators may be multiplexed within a hidden-photon coherence length to increase the sensitivity in this regime. Hidden-photon dark matter has an enormous range of possible frequencies, but current experiments search only over a few narrow pieces of that range. We find the potential sensitivity of our proposal is many orders of magnitude beyond current limits over an extensive range of frequencies, from 100 Hz up to 700 GHz and potentially higher. Show Partial Abstract