High-brightness electron beams with low energy spread at existing and future x-ray free-electron lasers are affected by various collective beam self-interactions and microbunching instabilities. The corresponding coherent optical radiation effects, e.g., coherent optical transition radiation, impede electron beam profile imaging and become a serious issue for all kinds of electron beam diagnostics using imaging screens. Furthermore, coherent optical radiation effects can also be related to intrinsically ultrashort electron bunches or the existence of ultrashort spikes inside the electron bunches. In this paper, we discuss methods to suppress coherent optical radiation effects both by electron beam profile imaging in dispersive beam lines and by using scintillation imaging screens in combination with separation techniques. The suppression of coherent optical emission in dispersive beam lines is shown by analytical calculations, numerical simulations, and measurements. Transverse and longitudinal electron beam profile measurements in the presence of coherent optical radiation effects in nondispersive beam lines are demonstrated by applying a temporal separation technique.