Parametric modeling and optimization of electromagnetic (EM) and multiphysics behaviors are very essential parts of the design process of microwave components. For EM/multiphysics design, the computational cost of directly using EM/multiphysics simulator is very expensive because the simulation-driven design requires repetitive EM/multiphysics evaluations due to the adjustments of the values of design parameters. This thesis proposes new techniques to speed up the parametric modeling and optimization of EM and multiphysics behaviors. In the first part of this thesis, a novel technique is proposed to develop a low-cost EM centric multiphysics parametric model for microwave components. In the proposed method, we use space mapping (SM) techniques to combine the computational efficiency of EM single physics simulation with the accuracy of the multiphysics simulation. Our proposed technique can achieve good accuracy for multiphysics parametric modeling with fewer multiphysics training data and less computational cost. As a further advancement, to accelerate the multiphysics design circle, we develop a novel parallel EM centric multiphysics optimization technique. The pole-residue-based transfer function is exploited to build an effective and robust surrogate model. A group of modified quadratic mapping functions is formulated to map the relationships between pole/residues of the transfer function and the design variables. Using our proposed technique, the surrogate model can be valid in a relatively large neighborhood which makes an effective and large optimization update in each optimization iteration. Our proposed multiphysics optimization technique takes a small number of iterations to obtain the optimal EM centric multiphysics response. In the third part of this thesis, a novel decomposition technique is proposed to address the challenges of EM parametric modeling with geometrical changes in a large range. A systematic and automatic algorithm based on second-order derivative information is proposed to decompose the modeling problem with a wide geometrical range into a set of sub-range modeling problems. Multiple artificial neural network (ANN) models, hereby referred to as sub-models are independently developed. A new technique is proposed to combine the developed sub-models to obtain a continuous overall model by solving the multi-dimensional discontinuity problem. The proposed method can obtain better model-accuracy with short model-development time.