This dissertation investigates machine learning (ML) methods for the prediction and extrapolation of electromagnetic (EM) responses, with the objective of substantially reducing the runtime and computational cost of conventional commercial simulation tools. Although ML-based surrogate models have shown promise in mixed-signal system design by approximating the nonlinear mapping between design parameters and response spaces, two key challenges persist: the need for reliable uncertainty quantification (UQ) due to prediction errors in neural networks (NNs), and the scarcity of training data. To address these challenges, this work develops a series of predictive models, UQ methods, and extrapolation frameworks. A Spectral Transposed Convolutional Neural Network (S-TCNN) with a two-dimensional kernel is proposed for predicting frequency responses from design parameters. A unified framework integrating the 2D S-TCNN with Gaussian Process (GP)-based extrapolation is further developed to reduce hyperparameter complexity. Moreover, a quantitative criterion for extrapolation range determination is established based on both sample distance and confidence intervals (CIs). To mitigate gradient vanishing during up-sampling, the input design parameters are mapped into a latent Gaussian space through cascaded GP layers. Additional contributions include trainable activation functions, a keep-kernel learning framework, and a training-set optimization strategy.