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When implementing high-order surface impedance boundary conditions in collocation boundary element method (BEM) with constant or linear elements, difficulties arise due to the computation of the curvature of the conductors and of the tangential derivatives of the unknowns. The use of nonuniform rational B-splines overcomes the above problems and gives a better representation of complex geometries. After comparing the previously derived formulation of high-order surface impedance boundary conditions with that obtained by other authors following a different approach, the resulting surface integral equations are discretized using nonuniform rational B-splines. Canonical problems of two circular and elliptical conductors are used for validation. Finally, the problem of the computation of per-unit-length parameters of sector-shaped cables is solved, showing the accuracy of the method.