Glenn O’Brien feels you should only wear dark brown shoes with navy suits — that, or just wear black shoes, which is reasonable and boring enough. Perhaps the urge to wear cognac with navy is simply instinct given that blue and orange are complementary colors and, well, cognac is close enough.
Still, a pleasing combination of colors doesn’t always inspire a pleasing clothing ensemble, especially with formal wear, but I think there’s more of a gray area than Glenn O’Brien would have us believe. And if it looks good to you and you’re the one wearing it, you’re probably okay.
Some good and bad examples below — intentionally left uncaptioned since I feel this matter is almost entirely decided by taste and not hard/fast style rules: