The ability of some RNA molecules to switch between different metastable conformations plays an important role in cellular processes. In order to identify such molecules and to predict their conformational changes one has to investigate the refolding pathways. As a qualitative measure of these transitions, the barrier height marks the energy peak along such refolding paths. We introduce a meta-heuristic to estimate such barriers, which is an NP-complete problem. To guide an arbitrary path heuristic, the method uses RNA shape representative structures as intermediate checkpoints for detours. This enables a broad but efficient search for refolding pathways. The resulting Shape Triples meta-heuristic enables a close to optimal estimation of the barrier height that outperforms the precision of the employed path heuristic.