First- and second-order surface impedance boundary conditions are introduced in the harmonic 2-D variational formulation based on the magnetic vector potential. The problem is discretized with isogeometric finite elements, a recent method that uses NURBS functions both to describe the geometry and the solution field. The method has the advantage that it allows an exact computation of the curvature of the geometry, which is required by high-order surface impedance boundary conditions. The proposed method is applied to the computation of per-unit-length parameters of multiconductor transmission lines.