Live modeling enables modelers to incrementally update models as they are running and get immediate feedback about the impact of their changes. Changes introduced in a model may trigger inconsistencies between the model and its run-time state (e.g., deleting the current state in a statemachine); effectively requiring to migrate the run-time state to comply with the updated model. In this paper, we introduce an approach that enables to automatically migrate such run-time state based on declarative constraints defined by the language designer. We illustrate the approach using Nextep, a meta-modeling language for defining invariants and migration constraints on run-time state models. When a model changes, Nextep employs model finding techniques, backed by a solver, to automatically infer a new run-time model that satisfies the declared constraints. We apply Nextep to define migration strategies for two DSLs, and report on its expressiveness and performance.