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This paper addresses the issue of how to meet the strict timing constraints of (soft) real-time virtualized applications while the Virtual Machine (VM) hosting them is undergoing a live migration. To this purpose, it is essential that the resource requirements of a migration are identified in advance, that appropriate resources are reserved to the process, and that multiple VMs sharing the same resources are temporally isolated from each other. The first issue is dealt with by introducing a stochastic model for the migration process. The other ones by introducing a methodology making use of proper scheduling algorithms (for both CPU and network) that allow for reserving resource shares to individual VMs. Also, an extensive set of simulations have been done by using traces of a VLC video server virtualized by using KVM on Linux. The traces have been obtained by patching KVM at the kernel level, and the same patch constitutes an important step towards the complete implementation of the proposed technique. The obtained results highlight the benefits of the proposed approach.