A coordinate measuring machine has a probe head, a calibrating body and an apparatus for recording and correcting measured values obtained by the probe head. A mechanical flexibility at predetermined points on the surface of the calibrating body is determined. The mechanical flexibility is stored in the apparatus in the form of a data record. The calibrating body is scanned point by point by means of the probe head in order to obtain the measured values. Thereafter, the probe head is calibrated by correcting the measured values using the data record. A similar approach can also be used on workpieces having a known mechanical flexibility.