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The universal line model (ULM) is a frequency dependent transmission-line model based on the method of characteristics in the phase domain. Although the ULM is known to produce highly accurate models for both overhead lines and underground cables, situations have been encountered where the pole identification for the propagation function fails. In this paper, we overcome the problem by basing the pole identification on trace fitting rather than mode fitting. This is achieved by introducing delayed basis functions in the vector fitting algorithm, followed by time-delay refinement and model-order reduction. In situations where the modes can be fitted without difficulty, the existing approach using modes obtained by a frequency-dependent transformation matrix remains the most accurate.