For roughness measurements, a passive roughness probe 118 having a probe tip 119 is exchanged into the measuring probe head of the coordinate measuring apparatus in lieu of the probe pin having a probe ball which is otherwise used to make coordinate measurements. The generation of the measurement points takes place while using the already available measured value transducers 23 in the probe head of the coordinate measuring apparatus. The desired surface characteristic variables are computed from the stored quasi-analog measured point sequence with the aid of a corresponding software module.