  This paper discusses and analyses two domain decomposition approaches for
electromagnetic problems that allow the combination of domains discretised by
either N\'ed\'elec-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 analytically and
numerically investigated. 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
N\'ed\'elec 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.
