Abstract: A superconducting magnet system comprises an annular cryogenic vessel (1) having an outer vacuum container (2) and containing a superconducting magnet (3) within an annular reservoir (4) containing liquid helium. A cryocooler (5) has a first stage (7) linked by a thermal link (9) to a thermal shield (6) within the vacuum space surrounding the reservoir (4) and a second stage (8) that serves to recondense evaporating helium gas from the reservoir (4). In the absence of special measures, such a cryocooled shield (6) would warm up quickly in the event of a power failure and would radiate heat onto the reservoir (4) causing all of the liquid helium to evaporate. However an inertial shield (11) is provided between the reservoir (4) and the thermal shield (6) in such a position that the outgoing helium gas from the reservoir (4) carries away the heat being transferred to the inertial shield (11) from the thermal shield (6) and thus slows down the rate at which the thermal inertial shield (11) warms up.