Real-time systems require a-priori temporal guarantees. While most of the normal operation in such a system is modeled using time-driven, hard-deadline sporadic tasks, event-driven behavior is modeled using aperiodic jobs with soft or no deadlines. To provide good Quality-of- Service for aperiodic jobs in the presence of sporadic tasks, aperiodic servers were introduced. Aperiodic servers act as a sporadic task and reserve a quota periodically to serve aperiodic jobs. The use of aperiodic servers in systems with caches is unsafe because aperiodic servers do not take into account, the indirect cache-related preemption delays that the execution of aperiodic jobs might impose on the lower-priority sporadic tasks, thus jeopardizing their safety. To solve this problem, we propose an enhancement to the aperiodic server that we call a Cache Delay Server. Here, each lower-priority sporadic task is assigned a delay quota to accommodate the cache-related preemption delay imposed by the execution of aperiodic jobs. Aperiodic jobs are allowed to execute at their assigned server priority only when all the active lower-priority sporadic tasks have a sufficient delay quota to accommodate it. Simulation results demonstrate that a Cache Delay Server ensures the safety of sporadic tasks while providing acceptable Quality-of-Service for aperiodic jobs. We propose a Integer Linear Program based approach to calculate delay quotas for sporadic tasks within a task set where Cache Delay Servers have been pre-assigned. We then propose algorithms to determine Cache Delay Server characteristics for a given sporadic task set. Finally, we extend the Cache Delay Server concept to multi-core architectures and propose approaches to schedule aperiodic jobs on appropriate Cache Delay Servers. Simulation results demonstrate the effectiveness of all our proposed algorithms in improving aperiodic job response times while maintaining the safety of sporadic task execution.