This paper discusses and analyzes two domain decomposition approaches for electromagnetic problems that allow the combination of domains discretized by either Nédélec-type polynomial finite elements or spline-based isogeometric analysis. The first approach is a new isogeometric mortar method and the second one is based on a modal basis for the Lagrange multiplier space, called state-space concatenation in the engineering literature. Spectral correctness and in particular inf-sup stability of both approaches are investigated numerically, and analytical results are obtained for the isogeometric mortar method. The new mortar method is shown to be unconditionally stable. Its construction of the discrete Lagrange multiplier space takes advantage of the high continuity of splines and does not have an analogue for Nédélec finite elements. On the other hand, the approach with modal basis is easier to implement but relies on application knowledge to ensure stability and correctness.