A multi-bath apparatus and method for cooling a superconductor includes both a cooling bath comprising a first cryogen and a shield bath comprising a second cryogen. The cooling bath surrounds the superconductor, and the shield bath surrounds the cooling bath. The cooling bath is maintained at a first pressure and subcooled, while the shield bath is maintained at a second pressure and saturated. The cooling bath and the shield bath are in a thermal relationship with one another, and the first pressure is greater the second pressure. Preferably, the cryogens are liquid nitrogen, and the superconductor is a high temperature superconductor, such as a current limiter. Following a thermal disruption to the superconductor, the first pressure is restored to the cooling bath and the second pressure is restored to the shield bath in order to restore the superconductor to a superconductive state.