Recently, an efficient constraint solving-based approach has been developed to detect logical faults in systems specified with classical finite state machines (FSMs). The approach is unsuitable to detect violations of time constraints. In this paper, we lift the approach to generated tests detecting both logical faults and violations of time constraints in systems specified with timed FSMs with timeouts (TFSMs-T). We propose a method to verify whether a given test suite is complete, i.e., it detects all the faulty implementations in a fault-domain and a method to generate a complete test suite. We conduct experiments to evaluate the scalability of the proposed methods.