Zero-dispersion stochastic resonance (ZDSR) in underdamped SQUIDs (superconducting quantum interference devices) has been investigated theoretically and by analogue electronic experiment. It is shown that, in common with the standard form of stochastic resonance (SR) that occurs at low frequencies in overdamped bistable systems, ZDSR can result in large noise-induced enhancements of the signal/noise ratio for a weak periodic signal. Unlike standard SR, however, ZDSR is to be anticipated over a vastly wider and tunable range of high frequencies in highly underdamped SQUIDs that need not necessarily be bistable.