With the rapid acceleration of global urbanization, progressively more natural disasters and public safety problems are encountered in cities. Previous studies have shown that highly resilient cities can promptly and effectively respond to disasters. Therefore, in this study, a mixed-methods approach to urban agglomeration resilience estimation is proposed. First, the particle swarm optimization algorithm is used to optimize the back propagation neural network in order to evaluate the resilience of subsystems, including economy, society, environment, and science and technology resilience subsystems. Then, the entropy weight method is integrated to obtain the urban agglomeration resilience. Finally, the kernel density estimation and Moran's I are utilized for comprehensive analysis of the dynamic evolution and spatial correlation of the urban agglomeration resilience. The Yangtze River Delta cities are adopted as a case study, and the results indicated that the resilience in the most developed urban agglomeration in China showed the pyramidal spatial distribution. From the perspective of evolution, the resilience level is constantly improving, and the differences among cities are gradually decreasing from 2015 to 2019. The results indicate that the model is valuable for evaluating urban resilience, and thus it can help policymakers formulate proposals to effectively improve the resilience of urban agglomerations.