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This paper presents a novel technique to develop combined neural network and transfer function models for parametric modeling of passive components. In this technique, the neural network is trained to map geometrical variables onto coefficients of transfer functions. A major advance is achieved in resolving the discontinuity problem of numerical solutions of the coefficients with respect to the geometrical variables. Minimum orders of transfer functions for different regions of geometrical parameter space are identified. Our investigations show that varied orders used for different regions result in the discontinuity of coefficients. The gaps between orders are bridged by a new order-changing module, which guarantees the continuity of coefficients and simultaneously maintains the modeling accuracy through a neural network optimization process. This technique is also expanded to include bilinear transfer functions. Once trained, the model provides accurate and fast prediction of the electromagnetic behavior of passive components with geometrical parameters as variables. Compared to conventional training methods, the proposed method allows better accuracy in challenging applications involving high-order transfer functions, wide frequency range, and large geometrical variations. Three examples including parametric modeling of slotted patch antennas, bandstop microstrip filters, and bandpass coupled-line filters are examined to demonstrate the validity of this technique.