In order to determine spatial coordinates of a multiplicity of measurement points along a contour of a measurement object, a probe head is provided with a probe element that is movably supported on the probe head. During movement of the probe head along the contour, position measuring values of the probe head and deflections of the probe element relative to the probe head are determined. Spatial coordinates for the measurement points along the contour are determined from the position measuring values and deflections. The probe element is kept in contact with the contour during movement of the probe head by using an actuator to produce a defined contact force. The contact force is set as a function of a differential acceleration of the probe element relative to the probe head.