The Mote in God's Eye by Larry Niven and Jerry Pournelle. It has two Navy starships discovering an alien civilization. From Amazon's review
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In the Mote the humans find an ancient civilization--at least one million years old--that has always been bottled up in their cloistered solar system for lack of a star drive. The Moties are welcoming and kind, yet rather evasive about certain aspects of their society. It seems the Moties have a dark problem, one they've been unable to solve in over a million years.
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This isn't perhaps quite what you were looking for, but it is very good.