An arrangement for damping vibrations during microscopic examinations of inorganic and organic material specimens in an evacuated measuring at low temperatures that are cooled by an electromechanical cryocooler suppresses transfer of vibrations from the cryocooler onto the specimen, the microscope table and the instrument table. The arrangement includes a cryocooler unit and a microscopy unit combined with a damping unit preferably located on a common longitudinal axis. The damping unit has a series arrangement of inter-coupled evacuable compensation chambers arranged along the longitudinal axis, the series arrangement being combined with damper groups, two of which act at least diametrically. A clamping unit is operationally connected to the damping unit at at least two points on the series arrangement. A tension force of the damping unit is adjustable.