A device for measuring the filling level of a medium--for example hydrogen--in a storage container of a storage device--for example a tank system. To provide a simple and direct possible way of accurately determining the filling level of the storage container even without knowing the amount of medium already discharged or irrespective of uncontrollable losses, the device is designed as a measuring device for measuring the nuclear magnetic resonance of the medium located in the storage container. For this purpose, the device has a measuring head with, for example, a permanent magnet and a measuring coil, via which a static magnetic field and an electromagnetic alternating field are generated in the measuring head. The electromagnetic alternating field is generated in a transmitter, which is connected to the measuring head by a bridge circuit. The values of the nuclear magnetic resonance of the stored medium measured by the measuring head are processed via the bridge circuit and an amplifier and displayed on a display device. A corresponding storage device and a suitable measuring method are also described.