  We place perturbative unitarity constraints on both the dimensionful and
dimensionless parameters in the Next-to-Minimal Supersymmetric Standard Model
(NMSSM) 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, neutralino and chargino mass
spectrum. Requiring higher order corrections to be no more than 41% of the
tree-level value, we obtain an upper bound of 20 TeV for the heavy Higgses and
12 TeV for the charginos and neutralinos outside defined fine-tuned regions. If
the corrections are no more than 20% of the tree-level value, the bounds are 7
TeV for the heavy Higgses and 5 TeV for the charginos and neutralinos. In all,
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.
