We study the anomalous magnetic moment of the muon in supersymmetric E 6 models and generic U(1)′ models to probe the model reactions and to find constraints on the large parameter space of these models. For future searches, by imposing the existing bounds coming from collider searches and theoretical considerations upon the U(1)′ model parameters, we examine the lightest Higgs boson mass mh and the mass of the additional Z boson mZ2 in such singlet extensions of the MSSM. We observed that not only supersymmetric E6 models but also generic U(1)′ models are sensitive to the imposition of the considered bounds. Indeed, without the muon anomaly constraints E6 models and generic U(1)′ models can predict mh as large as ∼150GeV and ∼180GeV, respectively. However, in addition to the mentioned constraints when a 1σ range for the anomalous magnetic moment of the muon is considered, we observe that generic U(1)′ models do not favor the mass of the lightest Higgs boson to be larger than 140 GeV; it should be smaller than 135 GeV in E6 models. © 2010 The American Physical Society.