High optical quality LiREF(4) (RE = Tb(3+), Dy(3+), Ho(3+), Er(3+) and Yb(3+)), PrF(3) and CeF(3) single crystals have been grown by the Czochralski technique. Their magneto-optical properties have been measured and analyzed in detail in the ultraviolet-visible wavelength region, and their figures of merit as Faraday rotators have been determined. CeF(3) presents superior properties above 300 nm, showing a figure of merit higher than that of the reference material, terbium-gallium-garnet, which is nowadays used in the visible-near infrared. PrF(3) is the best rotator for the 220-300 nm range. Towards shorter wavelength and in the vacuum ultraviolet, it is shown that the LiREF(4) crystals are unique rotators. Overall, the rare-earth fluoride single crystals studied here exhibit better properties than other materials considered so far, and therefore they have potential to cover the increasing demand for new and improved Faraday rotators in the ultraviolet-visible wavelength region.