We present a Higgs mass calculation at two-loop level based on the effective potential approach, which has been made available in the public computer codes SARAH and SPheno. The approach is based on generic formulae for the two-loop effective potential available from literature and can be applied to a large number of renormalisable supersymmetric models in a highly automated way. Three equivalent algorithms are presented, which are completely independent of one another. The code enables the study of the neutral Higgs boson masses at two loops in models beyond the MSSM with a similar precision as has been widely available in MSSM spectrum generators before the Higgs discovery in 2012. Details about the implementation, validation and limitations of the code are presented. This precision calculation is applied to four supersymmetric models, including the MSSM with large flavour violation, the MSSM with R-parity violation and the NMSSM, where we found throughout that the two-loop corrections give rise to significant contributions. An additional model, namely the MSSM extended by vectorlike quarks, is also studied. Here we do not focus only on the two-loop Higgs mass but also on the fine-tuning in the context of gauge mediated supersymmetry breaking. Finally, we present a collider study examining the production of exotic long-lived neutral particles at the LHC, assuming that these particles escape the detector. By applying analyses from the ATLAS and CMS collaborations that focus on a large missing transverse energy signature, we obtain upper cross section limits for arbitrary lifetimes. We found this method to be a complementary approach compared to traditional displaced vertex searches
