They can be used to discern the presence of a hot white dwarf or main sequence companion in orbit around a cooler star.
Most stars are actually relatively cool objects emitting much of their electromagnetic radiation in the visible or near-infrared part of the spectrum.
Ultraviolet radiation is the signature of hotter objects, typically in the early and late stages of their evolution.
Space-based solar observatories such as SDO and SOHO use ultraviolet telescopes (called AIA and EIT, respectively) to view activity on the Sun and its corona.
Weather satellites such as the GOES-R series also carry telescopes for observing the Sun in ultraviolet.