Safety and performance are key enablers for autonomous driving: on the one hand we want our autonomous vehicles (AVs) to be safe, while at the same time their performance (e.g., comfort or progression) is key to adoption. To effectively walk the tight-rope between safety and performance, AVs need to be risk-averse, but not entirely risk-avoidant. To facilitate safe-yet-performant driving, in this paper, we develop a task-aware risk estimator that assesses the risk a perception failure poses to the AV’s motion plan. If the failure has no bearing on the safety of the AV’s motion plan, then regardless of how egregious the perception failure is, our task-aware risk estimator considers the failure to have a low risk; on the other hand, if a seemingly benign perception failure severely impacts the motion plan, then our estimator considers it to have a high risk. In this paper, we propose a task-aware risk estimator to decide whether a safety maneuver needs to be triggered. To estimate the task-aware risk, first, we leverage the perception failure - detected by a perception monitor - to synthesize an alternative plausible model for the vehicle’s surroundings. The risk due to the perception failure is then formalized as the “relative” risk to the AV’s motion plan between the perceived and the alternative plausible scenario. We employ a statistical tool called copula, which models tail dependencies between distributions, to estimate this risk. The theoretical properties of the copula allow us to compute probably approximately correct (PAC) estimates of the risk. We evaluate our task-aware risk estimator using NuPlan and compare it with established baselines, showing that the proposed risk estimator achieves the best F1-score (doubling the score of the best baseline) and exhibits a good balance between recall and precision, i.e., a good balance of safety and performance.