A honing machine (100) for honing rotationally symmetrical bore holes in workpieces has a honing spindle (120), which is movably mounted in a spindle housing (130), is rotatable about a spindle axis (122) by means of a rotary drive (140), can be driven in an oscillating manner parallel to the spindle axis by means of a lifting drive (150) and has at a tool-side end means for securing a honing tool arrangement (200), which has a tool body (220) carrying at least one honing element, which by axial displacement of a tool-side expanding element (330) that is axially displaceable inside the tool body can be infed radially in relation to a tool axis (214) and can be pressed by a pressing force against an inner side of a bore hole to be machined. Also provided is an expanding system with a machine-side expanding rod (310), which is guided inside the honing spindle (120), is axially displaceable by means of an expanding drive (320) in relation to the honing spindle and has a tool-side end portion (314), for coupling onto the tool-side expanding element (330). The honing machine has a control device (400) for controlling operating movements of the honing spindle and the expanding system and a force measuring system with a force sensor (500) for generating a sensor signal proportional to the pressing force and a transmission path for transmitting the sensor signal or a signal derived therefrom to the control device. The force sensor (500) is arranged in the region of the tool-side end portion (314) of the machine-side expanding rod (310) and is connected to the control device by way of a telemetric transmission path.