Evolutionary tasks, specially refactoring, affect source code and object models, hindering correctness and conformance. Due to the gap between object models and programs, refactoring tasks get duplicated in commonly-used model-driven development approaches, such as Round-Trip Engineering. In this paper, we propose a formal approach to consistently refactor systems in a model-driven manner. Each object model refactoring applied by the user is associated with a sequence of behavior preserving program transformations, which can be semi-automatically performed to an initially conforming program. As a consequence, this foundation for model-driven refactoring guarantees behavior preservation of the target program, besides its conformance with the refactored object model. This approach is described in detail, along with its formal infrastructure, including a conformance relationship between object models and programs. A case study reveals evidence on issues that will surely recur in other model-driven development contexts.