We demonstrate a technique to reduce first-order Doppler shifts in crossed atomic/molecular and laser beam setups by aligning two counterpropagating laser beams as part of a Sagnac interferometer. Interference fringes on the exit port of the interferometer reveal minute deviations from perfect antiparallelism. Residual Doppler shifts of this method scale with the ratio v/(4d) of the typical atomic/molecular velocity v and the laser beam diameter d. The method is implemented for precision frequency calibration studies at deep-UV wavelengths, both in one- and two-photon excitation schemes: the 6s(2) --> 6s30p(3/2)J=1 line in Yb at 199 nm and the 4p(6) --> 4p(5)p[1/2](0) transition in Kr at lambda=212 nm. The achieved precision of 6 x 10(-10) is limited by the characteristics of the laser system.