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Abstract We analyze two minimal supersymmetric constrained models with low-energy vector-like matter preserving gauge coupling unification. In one we add to the MSSM spectrum a pair 5 + 5 ¯ $$ \mathbf{5}+\overline{\mathbf{5}} $$ of SU(5), in the other a pair 10 + 10 ¯ $$ \mathbf{10}+\overline{\mathbf{10}} $$ . We show that the muon g−2 anomaly can be explained in these models while retaining perturbativity up to the unification scale, satisfying electroweak and flavor precision tests and current LHC data. We examine also some related phenomenological features of the models, including Higgs mass, fine-tuning, dark matter and several LHC signatures. We stress that, at least for the 5 + 5 ¯ $$ \mathbf{5}+\overline{\mathbf{5}} $$ model, the parameter space consistent with g − 2 is entirely in reach of the LHC with a moderate increase in luminosity with respect to the current data set.