In some works, there's an antagonist who isn't known for being friendly with the protagonists. But sometimes, in situations when one of said protagonists (often the main/lead character, but supporting characters qualify as well) exhibits a heroic or otherwise positive character trait that sufficiently impresses the antagonist, the latter will not be above commending them or otherwise showing them approval of them or their character trait in question. It will particularly stand out if, previously, the antagonist was hostile or (more usually) simply dismissive of the targeted protagonist.
The action may usually be performed by the Noble Demon, but bonus points if it's the Big Bad delivering the praise. Note that the commendation is sincere, and is not an attempt by the villain to screw with the hero's head. The villain may also do it because they and the hero are Mirror Characters. It may also be a Pet the Dog moment to show the villain isn't such a bad guy after all (even if they won't admit it).
A Lawful Evil character, or a character with Evil Virtues, may have this as part of their personality, especially in a situation where Villains Never Lie. This can also be a trait of the Friendly Enemy (though depending on the work, it probably won't reach Go-Karting with Bowser levels). The Antagonist in Mourning may also do this as a tribute to the fallen hero (whether the hero is actually dead or not).
May frequently overlap with Combat Compliment and Worthy Opponent, where the praise is given during a fight. Compare Villain Takes an Interest, where the villain may become interested in being a mentor to the hero, and compare and contrast We Can Rule Together, where the villain tries to convince the hero that they would do better working together instead of against each other. Naturally there is also a large overlap with Sympathy for the Hero.
Compare Admiring the Abomination. Contrast Your Approval Fills Me with Shame, where a villain praises the hero for a negative trait or action and the hero feels disgusted as a result. Compare Villainous Valour when there's something admirable about the villain's efforts. Also different from Baddie Flattery, wherein the villain is still sincere in his praise of a positive trait but the praise comes across as utterly creepy and disturbing (though this might be a sister trope to that one). And, again, note the second paragraph above.
Please note: The character to whom the praise is given is generally a true-blue hero. If the Anti-Hero or the Anti-Villain is the recipient of the praise, it's a bit trickier since the former has villainous characteristics while skirting the line between good and evil, and the latter has heroic characteristics while still not being a clearly good guy. If the villain respects something relatively minor about the hero, it's The One Thing I Don't Hate About You. If the villain respects another unambiguous villain, that's Villain Cred. The Complete Monster may appear to apply this trope, but it is only out of pragmatic reasons since they have zero respect for the heroes or fellow villains whatsoever.
