Using the examples of laser-induced spin-reorientation phase transitions in TmFeO₃ and ErFeO₃ orthoferrites, we demonstrate that terahertz emission spectroscopy can obtain novel information about ultrafast laser-induced spin dynamics, which is not accessible by more common all-optical methods. The power of the method is evidenced by the fact that, in addition to the expected quasi-ferromagnetic and quasi-antiferromagnetic modes of the iron sublattices, terahertz emission spectroscopy enables detection of a resonance optically excited at an unexpected frequency of ∼0.3–0.35 THz. By recording how the amplitude and phase of the excited oscillations depend on temperature and applied magnetic field, we show that the unexpected mode has all the features of a spin resonance of the Fe³⁺ ions. We suggest that it can be assigned to transitions between the multiplet sublevels of the ⁶A₁ ground state of the Fe⁺³ ions occupying rare-earth positions.