An NMR magnet system uses a Stirling cooler having a cold head that extends into a housing of the system to cool a cold shield surrounding a cryogen vessel. The system may have a damper located between the cooler and the cold shield to reduce a transmission of vibration from the cooler to a magnet coil immersed in the cryogen. The damper may be passive, or may be part of an active damping system that uses an acceleration sensor to drive an active damper that compensates for cooler vibration. A compensation apparatus may use a stored characteristic of a signal distortion caused by the vibration and, in response to a trigger signal from the cooler, apply compensation to an excitation signal provided to a sample by an NMR probe in a bore of the magnet coil, or to an FID signal from the sample that is detected by the probe.