Stateful migration has emerged as the key solution to support latency-sensitive microservices at the edge while ensuring a satisfying experience for mobile users. In this paper, we address two relevant issues affecting stateful migration, namely, the migration of containerized microservices and that of the associated data connection. We do so by first introducing a novel network solution, based on OvS, that permits to preserve the established connection with mobile end users upon migrating a microservice. Then, using Podman and CRIU, we experimentally characterize the fundamental migration KPIs, i.e., migration duration and microservice downtime, and we devise an analytical model that, accounting for all the relevant real-world aspects of stateful migration, provides an accurate upper bound on such KPIs. We validate our model using real-world microservices, namely, MQTT Broker and Memcached, and show that it can predict KPIs values with an error that is up to 99.7% smaller than that yielded by the state of the art. Finally, we consider a UAV controller as relevant microservice use case and demonstrate how our model can be exploited to effectively configure the system parameters so that the required QoE level is met.