The invention relates to a polishing machine (10) and to a method for polishing optical waveguides, the polishing machine comprising a polishing disk (13) having a plug socket (14) for holding a plug with an optical waveguide, a polishing platform (15) for receiving an abrasive, a positioning device (17) for relative positioning of the polishing disk and of the polishing platform between a polishing position and a set-up position (16), and a drive device for executing a relative polishing movement between the polishing platform and the polishing disk in the polishing position, wherein the polishing machine has a cleaning device for applying dry ice to the polishing platform and/or to the polishing disk.