Taking into consideration the variability specific to the nowadays nanotechnologies, the fast extraction of parametric models is a must for the present VLSI and radio-frequency (RF)-integrated-circuit (IC) design environments. The major contribution of the paper is a new, effective methodology for the extraction of parametric compact models for passive RF integrated components with field effects, valid for high-frequency broad range. The proposed numeric method is systematically based on a dual approach, which provides two complementary approximations of the exact solution. Duality is applied both to the spaces where the discrete solution is found as well as to the open boundary conditions. The adjoint field technique is applied in an original manner to the finite-integral techniques to handle the parameter variability of the extracted model. The new method needs much less computing resources for modeling than other numerical methods.