A cooling device (20) has a cryostat (23) and a cold head (1), in particular, the cold head (1) of a pulse tube cooler. The cryostat (23) has a vacuum container (4) with a vacuum container wall (4a), wherein the vacuum container wall (4a) seals off a vacuum inside the vacuum container (4) from the environment. A flexible sealing section (6) connects the vacuum container wall (4a) directly or indirectly to the room temperature part (1a) of the cold head (1). The flexible sealing section (6) seals off the inside of the cryocontainer (2) from the environment. The cooling device further reduces mechanical coupling between the cold head and the cryostat, in particular, in order to enable performance of NMR measurements with fewer disturbances due to external vibrations.