A new higher order (HO) method of moments is proposed for high accuracy extraction of the resistance and inductance matrices in the multiconductor transmission lines (MTLs) of complex cross sections. The computational framework is based on the numerical solution of a surface–volume–surface electric field integral equation of magnetostatics. In order to achieve an exponentially efficient reduction in the error of the solution, HO geometrical representation of the conductor cross sections is accompanied with the discretization of the unknown field quantities on the conductor boundaries and cross sections with 1-D and 2-D HO polynomial basis functions, respectively. The methodology allows for extraction of the network parameters in broad ranges of frequencies for which resistive and inductive contributions to the impedance matrix vary within a wide dynamic range. Comparison of numerically computed currents to the currents obtained analytically for canonical transmission line configurations is performed. Solutions of the extraction problem for MTLs with complex cross sections are compared against the finite-element method solutions to demonstrate the efficiency of the proposed methodology.