  We study the anomalous magnetic moment of the muon, $g_\mu - 2 \equiv 2
a_\mu$, in the context of supersymmetric models beyond the CMSSM, where the
unification of either the gaugino masses $M_{1,2,3}$ or sfermion and Higgs
masses is relaxed, taking into account the measured mass of the Higgs boson,
$m_H$, the cosmological dark matter density and the direct detection rate. We
find that the model with non-unified gaugino masses can make a contribution
$\Delta a_\mu\sim 20 \times 10^{-10}$ to the anomalous magnetic moment of the
muon, for example if $M_{1,2} \sim 600$ GeV and $M_3\sim 8$ TeV. The model with
non-universal sfermion and Higgs masses can provide even larger $\Delta a_\mu
\sim 24 \times 10^{-10}$ if the sfermion masses for the first and the second
generations are $ \sim 400 $ GeV and that of the third is $ \sim 8 $ TeV. We
discuss the prospects for collider searches for supersymmetric particles in
specific benchmark scenarios illustrating these possibilities, focusing in
particular on the prospects for detecting the lighter smuon and the lightest
neutralino.
