Model checking timed systems may be negatively impacted by the presence of Zeno runs as counterexamples. Such runs contain an infinite number of discrete actions occurring in a finite time, which is unrealistic; therefore, these runs must be pruned during model checking. Given a model of a timed system and a property, parametric model checking aims at synthesizing timing valuations such that the model satisfies the property. A popular formalism for parametric timed model checking is parametric timed automata (PTAs), an extension of timed automata with unknown constants. We address the presence of Zeno runs in parametric model checking. We first show that the emptiness of the set of parameter valuations for which at least one counterexample run being non-Zeno is undecidable for PTAs. As a second contribution, we adopt a more pragmatic approach, and propose a procedure based on a transformation of PTAs into Clock Upper Bound PTAs to derive all valuations whenever it terminates, and some of them otherwise. We implemented our algorithm in IMITATOR, and we show that our method can be distributed over a cluster to further speedup the computation.