If I have a predicted RNA stem-loop of energy -0.30 kcal/mol, and another of -4.9 kcal/mol, how do I tell whether such a structure is a significantly stable structure or not? Our two competing hypotheses are that there is some structure with sufficient energetic stability to fold inside a cell, versus the one that there is not.
You can convert the $\Delta G$ values into equilibrium constants $K$ using the formula
$$ \Delta G = R T \ln K $$
This might help you understand what those energies roughly mean.
But the more important and also more difficult part is judging how good your predicted free energies actually are. I assume you used a secondary structure prediction program like Mfold to calculate this. They typically have a several parameters you can adjust like ion concentrations and temperature, you should make sure that you have some appropriate values here.
Without knowing anything more about your system or data I'd ignore the -0.3 kcal/mole result, the -4.9 kcal/mole structure could be formed, but I wouldn't regard this as certain.
Now, in the in vivo situation the whole thing gets far more complicated. The presence of RNA binding proteins, helicases and the generally rather complex environment in the cell makes it much harder to predict which secondary structures will actually form.
If you wanted to know for sure you could e.g. do SHAPE experiments on your RNA. This is a technique that also works in vivo.
Given an RNA sequence like the microRNA from arabidopsis ath-MIR447a
You can find its predicted secondary structure by doing RNA folding and measuring the free energy using Dr. Zuker's Unafold
This will show you the secondary structure most miRNA and transpon RNA like structures are stable variable hairpins.
If you seek to see how stable it is I wrote a thesis about this subject. Its missing from the internet at the moment and I don't have a backup copy. Essentially the location of bulges and complexity is also important for it to be viable. You can read the paper that was foundational for my work about a program called mirPred and use its features independent of their work.
If your secondary structure is not very stable than you can run a homology search for the organism you're interested in and then compare the energy and sequential features of the close relatives from mirPred.