Previous studies have revealed that paravirtualization imposes minimal performance overhead on High Performance Computing (HPC) workloads, while exposing numerous benefits for this field. In this study, we are investigating the memory hierarchy characteristics of paravirtualized systems and their impact on automatically-tuned software systems. We are presenting an accurate characterization of memory attributes using hardware counters and user-process accounting. For that, we examine the proficiency of <i>ATLAS</i>, a quintessential example of an autotuning software system, in tuning the <i>BLAS</i> library routines for paravirtualized systems. In addition, we examine the effects of paravirtualization on the performance boundary. Our results show that the combination of <i>ATLAS</i> and Xen paravirtualization delivers native execution performance and nearly identical memory hierarchy performance profiles. Our research thus exposes new benefits to memory-intensive applications arising from the ability to slim down the guest OS without influencing the system performance. In addition, our findings support a novel and very attractive deployment scenario for computational science and engineering codes on virtual clusters and computational clouds.