Future gravitational-wave detectors on Earth and on the Moon aim to access signals below 10Hz. On Earth, the Einstein Telescope - a next generation interferometric gravitational-wave detector — will extend the detection band down to 3 Hz. On the Moon, the Lunar Gravitational-wave Antenna will feature extremely sensitive accelerometers that can monitor the Moon’s body excited by gravitational waves from the lunar surface. Our cryogenic superconducting inertial sensor aims to meet requirements for deployment on the Moon and provide sensitive probes of suspended cryogenic objects in terrestrial gravitational-wave detectors. We aim for a displacement sensitivity at 1Hz of a few fm/√Hz, which is 3 orders of magnitude better than the state of the art.