A superconducting-coil apparatus according to the present invention comprises a normal-fluid helium bath, a superfluid helium bath, a channel connecting the two baths, superconducting coils contained in the superfluid helium bath, current lead wires extending from an exciting current source to the superconducting coils, through the channel, and a valve plug normally closing the channel and adapted to open the channel when the pressure inside the superfluid helium bath rises above a predetermined level. If the superconducting coils undergo quenching while they are being excited, the superfluid helium is gasified by Joule heat, produced in the coils. As a result, the pressure inside the superfluid helium bath increases, so that the valve plug is urged to open the channel due to the pressure difference. The gasified helium directly cools those portions of the lead wires which pass through the channel, thus these wire portions are prevented from being burned out.