Event-triggered control aims at reducing the communication load over the feedback link in networked control systems by adapting the information exchange to the current needs. This paper investigates the consequences of actuator saturation on the behavior of event-triggered PI control. Stability properties are derived using linear matrix inequalities (LMIs) which show how the stability of the event-triggered control loop depends on the selection of the event threshold. In order to overcome the potential performance degradation due to integrator windup caused by actuator saturation, the proposed scheme is extended by incorporating a static anti-windup mechanism. The results are illustrated by simulations.