Surface measuring device for measuring a surface of a workpiece has a device base body, and a measuring probe that by use of a feed apparatus is movable along a feed axis relative to a workpiece to be measured. The measuring probe has a probe base body and a probe element, connected to the probe base body, for scanning the workpiece in the direction of a measuring axis. The probe base body is connected to the measuring device base body via the feed apparatus. An oscillation damper is associated with the measuring probe, and is designed and configured for oscillation rate-dependent damping of oscillations of the probe base body of the measuring probe, and is active between the probe base body and the device base body.