Abstract: The competition between spin-orbit coupling (SOC) $\lambda$ and electron-electron interaction $U$ leads to a plethora of novel states of matter, extensively studied in the context of $t_{2g}^4$ and $t_{2g}^5$ materials, such as ruthenates and iridates. Excitonic magnets—the antiferromagnetic state of bounded electron-hole pairs-are prominent examples of phenomena driven by those competing energy scales. Interestingly, recent theoretical studies predicted that excitonic magnets can be found in the ground state of SOC $t_{2g}^4$ Hubbard models. Here we present a detailed computational study of the magnetic excitations in that excitonic magnet, employing one-dimensional chains (via density matrix renormalization group) and small two-dimensional clusters (via Lanczos). Specifically, first we show that the low-energy spectrum is dominated by a dispersive (acoustic) magnonic mode, with extra features arising from the $\lambda =0$ state in the phase diagram. Second, and more importantly, we found a novel magnetic excitation forming a high-energy optical mode with the highest intensity at wave-vector $q\to 0$. In the excitonic condensation regime at large $U$, we also have found a novel high-energy $\pi$ mode composed solely of orbital excitations. These features do not appear all together in any of the neighboring states in the phase diagram and thus constitute unique fingerprints of the $t_{2g}^4$ excitonic magnet, of importance in the analysis of neutron and resonant inelastic x-ray scattering experiments.