Endplate moment connections with shape memory alloy (SMA) bolts provide self-centering for the seismic resilience of structures. Predicting the self-centering response of these new beam-column connections, which have not been codified yet, requires conducting experimental tests or detailed continuum finite-element simulations. Computationally efficient predictive tools are needed to facilitate the analysis, design, and assessment of self-centering connections and moment frames. In this paper, artificial neural networks (ANNs) are used to develop a MATLAB tool for predicting the moment-rotation backbone and self-centering response of extended endplate connections with SMA bolts. As the input for the neural networks, the predictive model development employs a design database of response parameters from 72 finite-element (FE) models and experimental tests of seven beam-column connection specimens. Neural networks are trained for seven response parameters, and the trained networks are used to develop a graphical user interface (GUI). The coefficient of determination for the trained ANNs is in the range of 0.92 to 0.99, indicating acceptable prediction accuracy. Furthermore, optimization studies using a multiobjective genetic algorithm are performed, seeking the minimization of material use (steel and SMA) and improved connection-response characteristics (i.e., stiffness, strength, and ductility). A phenomenological model of SMA connections is also developed in OpenSees. The use of the ANN-based predictive tool for accurate and efficient modeling of SMA-based connections and self-centering moment-resisting frames is illustrated. The computation time for predicting the moment-rotation response of a typical SMA connection is significantly reduced from seven hours in ANSYS to only three minutes in OpenSees while providing the same level of response prediction accuracy. Furthermore, the optimization results are confirmed by performing nonlinear pushover and response history analyses.