Real-time systems, such as real-time operating systems, often have to be able to cope with an unbounded number of similar components. These systems fall in the class of parameterized systems. Especially in safety-critical areas, formal verification ensures that they behave correctly in all cases. However, the machine-assisted verification of parameterized real-time systems is hard because automatic verification techniques (such as model checking) can be employed directly only for finite instances of a system and are thus incomplete. To overcome this problem, we provide a framework for the mechanical, comprehensive, and semi-automatic verification of parameterized real-time systems. At its core, we employ the process calculus Timed CSP. We provide an interactive theorem proving environment enhanced with debugging capabilities using automatic verification techniques. Thus, finite instances can be checked and debugged with automatic tool support. Then, given the evidence that the overall parameterized real-time system behaves correctly, our theorem proving environment facilitates its semi-automatic, comprehensive verification.