  We study Higgs boson masses in supersymmetric models with an extra U(1)
symmetry to be called U(1)$^{\prime}$. Such extra gauge symmetries are urged by
the $\mu$ problem of the MSSM, and they also arise frequently in low-energy
supersymmetric models stemming from GUTs and strings. We analyze mass of the
lightest Higgs boson and various other particle masses and couplings by taking
into account the LEP bounds as well as the recent bounds from Tevatron
experiments. We find that the $\mu$-problem motivated generic low-energy
U(1)$^{\prime}$ model yields Higgs masses as large as $\sim 200\ {\rm GeV}$ and
violate the Tevatron bounds for certain ranges of parameters. We analyze
correlations among various model parameters, and determine excluded regions by
both scanning the parameter space and by examining certain likely parameter
values. We also make educated projections for LHC measurements in light of the
Tevatron restrictions on the parameter space. We further analyze certain
benchmark models stemming from E(6) breaking, and find that they elevate Higgs
boson mass into Tevatron's forbidden band when U(1)$^{\prime}$ gauge coupling
takes larger values than the one corresponding to one-step GUT breaking.
