Coupled-cluster as well as equation-of-motion coupled-cluster methods play an important role whenever high accuracy is warranted. Concerning excitation energies, consideration of triple excitations is typically required to reach an accuracy better than 0.1-0.3 eV. In the context of strong magnetic fields such accuracy is needed for the prediction of spectra of strongly magnetized White Dwarfs. In addition it turns out that in order to correctly model the behavior of energies with respect to the magnetic field strength, triple excitations are required. Due to avoided crossings which are extremely often encountered in the context of strong magnetic fields, double-excitation character can be transferred between electronic states of the same symmetry. We report an implementation of the full finite-field coupled-cluster with single, double, and triple substitutions (CCSDT) and the equation-of-motion-CCSDT models and apply them to the prediction of field-dependent transition wavelengths for sodium as well as to the four lowest singlet states of the CH+ molecule in a strong magnetic field.