What are the precise meanings of the Greek words hyperēphanos and hyperphroneō?

Well, I’ve gone to LSJ. The definitions I find there are:

ὑπερφρονέω

1. Group I
1. to be over-proud, have high thoughts (Aeschylus)
1. to be proud in or of something (Herodotus)
2. overlook, look down upon, despise (Aeschylus)
1. (passive) to be despised (Thucydides)
3. think slightly of (Eurypides)
2. Group II
1. surpass in knowledge (Aeschines); excel in wisdom (Hippocrates)

ὑπερήφανος

1. overweening, arrogant (Hesiod)
1. bear oneself proudly; living sumptuously, prodigally or insolently, brutally
2. magnificent, splendid (Plato)
1. sublime (Damascius)

As you can see, hyperphroneō “above-think” can mean both “be more knowledgeable than” or “think that you’re above”; but from those definitions, that seems to have been about generic pride, rather than overestimating one’s abilities.