Caches have become invaluable for higher-end architectures to hide, in part, the increasing gap between processor speed and memory access times. While the effect of caches on timing predictability of single real-time tasks has been the focus of much research, bounding the overhead of cache warm-ups after preemptions remains a challenging problem, particularly for data caches. This paper makes multiple contributions. 1) We bound the penalty of cache interference for real-time tasks by providing accurate predictions of data cache behavior across preemptions, including instruction cache and pipeline effects. We show that, when considering cache preemption, the critical instant does not occur upon simultaneous release of all tasks. 2) We develop analysis methods to calculate upper bounds on the number of possible preemption points for each job of a task. To make these bounds tight, we consider the entire range between the best-case and worst-case execution times (BCET and WCET) of higher priority jobs. The effects of cache interference are integrated into the WCET calculations by using a feedback mechanism to interact with a static timing analyzer. Significant improvements in tightening bounds of up to an order of magnitude over two prior methods and up to half a magnitude over a third prior method are obtained by experiments for (a) the number of preemptions, (b) the WCET and (c) the response time of a task. Overall, this work contributes by calculating the worst-case preemption delay under consideration of data caches.