We consider residual-based a posteriori error estimators for the heterogeneous Maxwell equations using isotropic as well as anisotropic meshes. The continuous problem is approximated by using conforming approximated spaces with minimal assumptions. Lower and upper bounds are obtained under standard assumptions on the meshes. The lower bound holds unconditionally, while the upper bound depends on alignment properties of the meshes with respect to the solution. In particular for isotropic meshes the upper bound also holds unconditionally. A numerical test is presented which confirms our theoretical results.