In this paper, we focus on an a posteriori residual-based error estimator for the T/Ω magnetodynamic harmonic formulation of the Maxwell system. Similarly to the A/φ formulation , the weak continuous and discrete formulations are established, and the well-posedness of both of them is addressed. Some useful analytical tools are derived. Among them, an ad-hoc Helmholtz decomposition for the T/Ω case is derived, which allows to pertinently split the error. Consequently, an a posteriori error estimator is obtained, which is proven to be reliable and locally efficient. Finally, numerical tests confirm the theoretical results.