This paper defines a real-time rewriting logic semantics for a significant subset of Ptolemy II discrete-event models. This is a challenging task, since such models combine a synchronous fixed-point semantics with hierarchical structure, explicit time, and a rich expression language. The code generation features of Ptolemy II have been leveraged to automatically synthesize a Real-Time Maude verification model from a Ptolemy II design model, and to integrate Real-Time Maude verification of the synthesized model into Ptolemy II. This enables a model-engineering process that combines the convenience of Ptolemy II DE modeling and simulation with formal verification in Real-Time Maude. We illustrate such formal verification of Ptolemy II models with three case studies.