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We present the prediction of the electroweak $\rho$ parameter and the $W$boson mass in the CP-violating Next-to-Minimal Supersymmetric extension of theStandard Model (NMSSM) at the two-loop order. The $\rho$ parameter iscalculated at the full one-loop and leading and sub-leading two-loop order$\mathcal{O}(\alpha + \alpha_t\alpha_s +\left(\alpha_t+\alpha_\lambda+\alpha_\kappa\right)^2)$. The new $\Delta \rho$prediction is incorporated into a prediction of $M_W$ via a full supersymmetric(SUSY) one-loop calculation of $\Delta r$. Furthermore, we include all knownstate-of-the-art SM higher-order corrections to $\Delta r$. By comparingresults for $\Delta \rho$ obtained using on-shell (OS) and$\overline{\mathrm{DR}}$ renormalization conditions in the top/stop sector, wefind that the scheme uncertainty is reduced at one-loop order by 55%, attwo-loop $\mathcal{O}(\alpha_s\alpha_t)$ by 22%, and at two-loop$\mathcal{O}(\alpha_t+\alpha_\kappa+\alpha_\lambda)^2$ by 16%, respectively.The influence of the two-loop results on the $M_W$ mass prediction is found tobe sub-leading. The new calculation is made public in the computer program$\mathrm{\tt NMSSMCALC}$. We perform an extensive comparison in the $W$-mass,Higgs boson mass and the muon anomalous magnetic moment prediction between ourcalculation and three other publicly available tools and find very goodagreement provided that the input parameters and renormalization scales aretreated in the same way. Finally, we study the impact of the CP-violatingphases on the $W$-mass prediction which is found to be smaller than the overallsize of the SUSY corrections.

The ${\cal O}(\alpha_t+\alpha_\lambda+\alpha_\kappa)^2$ Correction to  the $\rho$ Parameter and its Effect on the W Boson Mass Calculation in the  Complex NMSSM