Stringent limits are set on the long-lived lepton-like sector of the phenomenological minimal supersymmetric standard model (pMSSM) and the anomaly-mediated super-symmetry breaking (AMSB) model. The limits are derived from the results presented in a recent search for long-lived charged particles in proton-proton collisions, based on data collected by the CMS detector at a centre-of-mass energy of 8 TeV at the Large Hadron Collider. In the pMSSM parameter sub-space considered, 95.9% of the points predicting charginos with a lifetime of at least 10 ns are excluded. These constraints on the pMSSM are the first obtained at the LHC. Charginos with a lifetime greater than 100 ns and masses up to about 800 GeV in the AMSB model are also excluded. The method described can also be used to set constraints on other models.