Measurement accuracy during determination of the thickness of rolling stock, in particular a rolling strip or a metal plate, is remotely measured using a base measurement value for the thickness obtained by a radiation measurement system having a radiation source and a radiation detector, both carried by a holding mechanism. A reference measurement value for the thickness is measured by an ultrasonic measurement head that is likewise arranged on the holding mechanism. The reference measurement value is used to eliminate the influence of errors on the base measurement value.