We present high-resolution images of the Sun in the near-ultraviolet spectral range between 214 nm and 397 nm as obtained from the first science flight of the 1 m SUNRISE balloon-borne solar telescope. The quiet-Sun rms intensity contrasts found in this wavelength range are among the highest values ever obtained for quiet-Sun solar surface structures—up to 32.8% at a wavelength of 214 nm. We compare the rms contrasts obtained from the observational data with theoretical intensity contrasts obtained from numerical magnetohydrodynamic simulations. For 388 nm and 312 nm the observations agree well with the numerical simulations whereas at shorter wavelengths discrepancies between observed and simulated contrasts remain.