We present the results of a spectroscopic monitoring campaign of the OB-star companions to the eclipsing X-ray pulsars SMC X-1, LMC X-4 and Cen X-3. High-resolution optical spectra obtained with UVES on the ESO Very Large Telescope are used to determine the radial-velocity orbit of the OB (super)giants with high precision. The excellent quality of the spectra provides the opportunity to measure the radial-velocity curve based on individual lines, and to study the effect of possible distortions of the line profiles due to e.g. X-ray heating on the derived radial-velocity amplitude.