In the quest to improve services, companies offer customers the opportunity to interact with agents through contact centers, where the communication is mainly text-based. This has become one of the favorite channels of communication with companies in recent years. However, contact centers face operational challenges, since the measurement of common proxies for customer experience, such as knowledge of whether customers have abandoned the queue and their willingness to wait for service (patience), are subject to information uncertainty. We focus this research on the impact of a main source of such uncertainty: silent abandonment by customers. These customers leave the system while waiting for a reply to their inquiry, but give no indication of doing so, such as closing the mobile app of the interaction. As a result, the system is unaware that they have left and waste agent time and capacity until this fact is realized. In this paper, we show that 30%-67% of the abandoning customers abandon the system silently, and that such customer behavior reduces system efficiency by 5%-15%. To do so, we develop methodologies to identify silent-abandonment customers in two types of contact centers: chat and messaging systems. We first use text analysis and an SVM model to estimate the actual abandonment level. We then use a parametric estimator and develop an expectation-maximization algorithm to estimate customer patience accurately, as customer patience is an important parameter for fitting queueing models to the data. We show how accounting for silent abandonment in a queueing model improves dramatically the estimation accuracy of key measures of performance. Finally, we suggest strategies to operationally cope with the phenomenon of silent abandonment.