A device (1) for holding a tool holder for face milling a brake disc present on a vehicle, the device (1) comprising a coupling section (5) which can be connected to a shaft or hub rotating around the axis of rotation, as well as a support (9) for supporting the tool holder, and means for holding the tool holder at right angles to the axis of rotation. These holding means comprise a socket joint (13) being connected to the coupling section (5) and to the support (9). The device (1) further includes adjusting means for adjusting the support at right angles to the axis of rotation and a protractor (31) which is attached to the support (9) and produces a signal that is indicative of the orientation of the support relative to an imaginary horizontal face.