  The Next-to-Minimal Supersymmetric Standard model (NMSSM) appears as an
interesting candidate for the interpretation of the Higgs-measurement at the
LHC and as a rich framework embedding physics beyond the Standard Model. We
consider the renormalization of the Higgs sector of this model in its
$\mathcal{CP}$-violating version, and propose a renormalization scheme for the
calculation of on-shell Higgs masses. Moreover, the connection between the
physical states and the tree-level ones is no longer trivial at the radiative
level: a proper description of the corresponding transition thus proves
necessary in order to calculate Higgs production and decays at a consistent
loop order. After discussing these formal aspects, we compare the results of
our mass calculation to the output of existing tools. We also study the
relevance of the on-shell transition-matrix in the example of the $h_i \to
\tau^+ \tau^-$ width. We find deviations between our full prescription and
popular approximations that can exceed $10\%$.
