We present a framework for TCTL-preserving translations between time-dependent modeling formalisms. The framework guarantees that once the original and the translated system are in one-by-many correspondence relation (a notion of behavioral equivalence between timed transition systems) then TCTL properties of the original system can be transformed too while preserving the verification answers. We demonstrate the usability of the technique on two reductions from bounded timed-arc Petri nets to networks for timed automata, providing unified proofs of the translations implemented in the verification tool TAPAAL. We evaluate the efficiency of the approach on a number of experiments: alternating bit protocol, Fischer’s protocol, Lynch–Shavit protocol, MPEG-2 encoder, engine workshop and medical workflow. The results are encouraging and confirm the practical applicability of the approach.