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The authors present, for the first time, a comprehensive theory for self-adjoint S-parameter sensitivities of non-homogenous transmission-line modelling problems. They show that wideband S-parameter sensitivities can be efficiently calculated without carrying out any adjoint simulations. The Np original simulations used to calculate the S-parameters of an Np-port electromagnetic structure supply the sensitivities as well. The authors also present their approach for two different types of nodes utilised in transmission-line modelling. The efficiency and accuracy of their algorithms are illustrated through a number of examples. Good match is obtained between their self-adjoint sensitivities and those calculated using finite differences at the response level.