Thermodynamic RNA secondary structure prediction is an important recipe for the latest generation of functional non-coding RNA finding tools. However, the predicted energy is not strong enough by itself to distinguish a single functional non-coding RNA from other RNA. Here, we analyze how well an RNA molecule folds into a particular structural class with a restricted folding algorithm called Thermodynamic Matcher (TDM). We compare this energy value to that of randomized sequences. We construct and apply TDMs for the non-coding RNA families RNA I and hammerhead ribozyme type III and our results show that using TDMs rather than universal minimum free energy folding allows for highly significant predictions.