We place perturbative unitarity constraints on both the dimensionful and dimensionless couplings in the Next-to-Minimal Supersymmetric Standard Model Higgs Sector. These constraints, plus the requirement that the singlino and/or Higgsino constitutes at least part of the observed dark matter relic abundance, generate upper bounds on the Higgs and neutralino/chargino mass spectrum. We obtain an upper bound of 12 TeV for the charginos and neutralinos and 20 TeV for the heavy Higgses outside defined fine-tuned regions. By using the NMSSM as a template, we describe a method which replaces naturalness arguments with more rigorous perturbative unitarity arguments to get a better understanding of when new physics will appear.