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This paper presents a novel sensitivity-analysis-based adjoint neural-network (SAANN) technique to develop parametric models of microwave passive components. This technique allows robust parametric model development by learning not only the input-output behavior of the modeling problem, but also derivatives obtained from electromagnetic (EM) sensitivity analysis. A novel derivation is introduced to allow complicated high-order derivatives to be computed by a simple artificial neural-network (ANN) forward-back propagation procedure. New formulations are deduced for exact second-order sensitivity analysis of general multilayer neural-network structures with any numbers of layers and hidden neurons. Compared to our previous work on adjoint neural networks, the proposed SAANN is easier to implement into an existing ANN structure. The proposed technique allows us to obtain accurate and parametric models with less training data. Another benefit of this technique is that the trained model can accurately predict derivatives to geometrical or material parameters, regardless of whether or not these parameters are accommodated as sensitivity variables in EM simulators. Once trained, the SAANN models provide accurate and fast prediction of EM responses and derivatives used for high-level optimization with geometrical or material parameters as design variables. Three examples including parametric modeling of coupled-line filters, cavity filters, and junctions are presented to demonstrate the validity of this technique.