In this work, Nédélec elements on locally refined meshes with hanging nodes are considered. A crucial aspect is the orientation of the hanging edges and faces. For non-orientable meshes, no solution or implementation has been available to date. The problem statement and corresponding algorithms are described in great detail. As a model problem, the time-harmonic Maxwell’s equations are adopted because Nédélec elements constitute their natural discretization. The algorithms and implementation are demonstrated through two numerical examples on different uniformly and adaptively refined meshes. The implementation is performed within the finite element library deal.II .