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 $v∕\left(4d\right)$ 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 $6s^2\to 6s30p_{3∕2}$ $J=1$ line in Yb at $199\mathrm{nm}$ and the $4p^6\to 4p^{5}p{[1∕2]}_0$ transition in Kr at $\lambda =212\mathrm{nm}$ . The achieved precision of $6\times {10}^{-10}$ is limited by the characteristics of the laser system.