Event-based prospective memory (PM) involves remembering to perform intended actions after a delay. An important theoretical issue is whether and how people monitor the environment to execute an intended action when a target event occurs. Performing a PM task often increases the latencies in ongoing tasks. However, little is known about the reasons for this cost effect. This study uses diffusion model analysis to decompose monitoring processes in the PM paradigm. Across 4 experiments, performing a PM task increased latencies in an ongoing lexical decision task. A large portion of this effect was explained by consistent increases in boundary separation; additional increases in nondecision time emerged in a nonfocal PM task and explained variance in PM performance (Experiment 1), likely reflecting a target-checking strategy before and after the ongoing decision (Experiment 2). However, we found that possible target-checking strategies may depend on task characteristics. That is, instructional emphasis on the importance of ongoing decisions (Experiment 3) or the use of focal targets (Experiment 4) eliminated the contribution of nondecision time to the cost of PM, but left participants in a mode of increased cautiousness. The modeling thus sheds new light on the cost effect seen in many PM studies and suggests that people approach ongoing activities more cautiously when they need to remember an intended action.