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This paper presents a novel technique for the calculation of the proper modes of 2D or 3D non-radiating dielectric (NRD) components for mm-wave applications. The novelty of this technique is the use of an integral equation method, in conjunction with a special algorithm for solving the resulting homogeneous matrix problem. This algorithm consists in the tracking of the matrix eigenvalues in the complex plane, when varying either the frequency or the mode propagation constant, and proved to be faster and more reliable than standard approaches, based on the direct search of the determinant zeros. Its effectiveness is demonstrated through the determination of the dispersion diagram of an NRD guide and the calculation of the resonance frequencies of a dielectric resonator.