This paper presents the results of investigations on the accuracy of contact point identification during coordinate measurement, which is crucial in the context of the Industry 4.0 concept. In particular, the effects of swivel length and probe declination angle during measurement were analyzed. In the experiments, deviations from the expected coordinates (0,0,0) of the contact point were analyzed for different rotational angles of the probing head. It was found that the recommended vertical positioning of the stylus at an angle of A = 0° might have introduced some insignificant errors. Increasing angle A up to 15° generated additional errors of negligible values in comparison with the measurement accuracy of the CMM. However, an increase in angle A up to 90° introduced additional errors as high as 10 μm. This contact point identification error will have a certain effect on the best fitting element and subsequent calculations and on the respective measurement results.