As a key component in micro/nano machining and measurement equipment, the Z-axis is subject to manufacturing and assembly errors, which introduce six-degree-of-freedom (6-DOF) geometric errors that directly degrade metrology and machining precision. A measurement method is proposed for the Z-axis linear and angular errors based on laser interferometry and autocollimation. An error compensation model is established by analyzing the spatial position errors of functional points on the CMM, founded on Abbe and Bryan principles. The proposed method was implemented on a micro/nano-CMM, where an online 6-DOF error measurement system were developed. Measurements were performed along the Z-axis on a grade 0 gauge block with a thickness of 8 mm using the CMM. The results show that the measurement standard deviation and indication error were reduced by 54.6% and 54.3%, respectively, after compensation. This method and system provide a reliable solution for improving the measurement and machining accuracy of CMMs and other precision equipment.