  High-$Q$ whispering gallery mode microresonators are cornerstones to develop
compact coherent sources like single frequency lasers or frequency combs. This
work reports a detailed characterization of a whispering gallery mode
microsphere in the near ultraviolet. Light coupling in the resonator is obtain
thanks to a robust angle-polished fiber allowing to investigate the different
coupling regimes. An intrinsic $Q_0$-factor of $2.2 \times 10^8$ and a finesse
of $7.3 \times 10^4$ are reported at a wavelength of 420 nm. Physical
mechanisms contributing to the $Q_0$-factor are discussed and routes to improve
the performances are drawn. Such high-$Q$ factor and high finesse are key
ingredients to ease the study of photonic devices based on WGM microresonators.
