A system for maintaining a high vacuum in a vacuum enclosure such as cryostat, for example, is described. The system includes a high-vacuum pump having an input that is connected to the cryostat and an output. A vacuum vessel is connected to the output of the high-vacuum pump. A second vacuum pump is connectable to the vacuum vessel. The system is operated such that the high-vacuum pump maintains the cryostat at a high vacuum and the second vacuum pump is periodically operated to maintain the pressure of the vacuum vessel below a threshold pressure. The second vacuum pump may be either permanently connected to, or removable from, the vacuum vessel. The vacuum vessel acts to maintain the output of the high-vacuum pump within a suitable pressure range. This removes the need for the output of the high-vacuum pump to be connected to a continuously operating, second-stage vacuum pump. Furthermore, the second vacuum pump is only required to be operated periodically in order to maintain the pressure in the vacuum vessel below the threshold pressure.