Purpose -In this paper, the aim is to propose a residual-based error estimator to evaluate the numerical error induced by the computation of the electromagnetic systems using a finite element method in the case of the harmonic A-w formulation. Design/methodology/approach -The residual based error estimator used in this paper verifies the mathematical property of global and local error estimation (reliability and efficiency). Findings -This estimator used is based on the evaluation of quantities weakly verified in the case of harmonic A-w formulation. Originality/value -In this paper, it is shown that the proposed estimator, based on the mathematical developments, is hardness in the case of the typical applications.