The recently developed equation-of-motion coupled-cluster (EOMCC) method with singles, doubles, and a selected set of triples defined through active orbitals (EOMCCSDt) is applied to the excited-state potential energy curves of the CH+ ion. The results are compared with the EOMCCSD (EOMCC singles and doubles), EOMCCSDT (EOMCC singles, doubles, and triples), and full configuration interaction results. It is demonstrated that the EOMCCSDt method provides the excited-state potentials of the EOMCCSDT quality and that the EOMCCSDt and EOMCCSDT methods restore the asymptotic degeneracy of excited states, which is broken by the EOMCCSD and other EOMCC doubles models.