Since the concept of toughness was introduced to transportation systems, transportation system toughness has received extensive attention from researchers in the field of transportation worldwide. In this paper, a methodology for quantifying and assessing the toughness of urban transportation systems is proposed in the context of the New Crown epidemic. Firstly, the definition of urban transportation system toughness in this context is clarified, and the entropy evaluation method is applied to construct the performance curve of urban transportation systems over time. Then, it is proposed to quantify the system’s resistance, recovery, and adaptive ability in terms of the change in the cumulative amount of system performance. Finally, the three characteristic abilities of system toughness are organically combined to obtain a comprehensive assessment of system toughness. Example calculations and analyses are carried out in four Chinese cities with different levels of development, and the results show that the performance of urban transportation systems is positively correlated with their levels of development, and all of them fluctuate greatly under the influence of the epidemic, but Wuhan has the strongest resistance and recovery ability of the transportation system, and shows the highest toughness, followed by Lanzhou, Changchun, and Shanghai. The system toughness quantification and assessment methods proposed in this paper provide a reference for research on improving the ability of urban transportation systems to deal with multiple uncertainty disturbances.