A conventional bridge-type coordinate measuring machine (CMM) with an opto-tactile fibre probe for the measurement of microstructures has been equipped with a metrology frame in order to reduce its measurement uncertainty. The frame contains six laser interferometers for high-precision position and guiding deviation measurements, a Zerodur cuboid with three measuring surfaces for the laser interferometers to which the fibre probe is fixed, and an invar frame which supports the measuring objects and to which the reference mirrors of the interferorneters are fixed. The orthogonality and flatness deviations of the Zerodur measuring surfaces have been measured and taken into account in the equation of motion of the probing sphere. As a first performance test, the flatness of an optical flat has been measured with the fibre probe. Measuring-depth-dependent and probing-force-dependent shifts of the probing position were observed. In order to reduce the scattering of the probing points, 77 measurements were averaged for one coordinate point to be measured. This has led to measuring times of several hours for one plane and strong thermal drifts of the measured probing points.