Optimization and modeling techniques are the essential part of design process of microwave filters. Space mapping is a recognized method for speeding up electromagnetic (EM) optimization, and has been applied to microwave filter design. In the first part of this thesis, a cognition-driven formulation of space mapping method is proposed and applied to EM-based filter optimization to increase optimization efficiency and the ability to avoid being trapped in local minima. This new technique utilizes two sets of intermediate feature space parameters, including feature frequency parameters and ripple height parameters. The design variables are mapped to the feature frequency parameters, which are further mapped to the ripple height parameters. By formulating the cognition-driven optimization directly in the feature space, our method increases optimization efficiency and the ability to avoid being trapped in local minima. In the second part of this thesis, a multivalued neural network is proposed to solve the non-uniqueness (multivalued) problem in inverse modeling. Our proposed technique can be effectively applied to parameter extraction of microwave filters. We propose a multivalued neural network inverse modeling technique to associate a single set of electrical parameters with multiple sets of geometrical or physical parameters. One set of geometrical or physical parameters is called one value of our proposed inverse model. Our proposed multivalued neural network is structured to accommodate multiple values for the model output. We also propose a new training error function to focus on matching each training sample using only one value of our proposed inverse model, while other values are free and can be trained to match other contradictory samples. In this way, our proposed multivalued neural network can learn all the training data by automatically redirecting contradictory information into different values of the proposed inverse model. Therefore, our proposed technique can solve the non-uniqueness problem in a simpler and more automated way compared to existing ANN inverse modeling techniques. Both proposed techniques in this thesis are illustrated by several microwave filter examples. Our proposed techniques can be used in the design and tuning processes of microwave filters.