Combat Compliment

Most fights either have the combatants forgoing conversation to focus on kicking ass, or engaging in Trash Talk, either as psychological warfare to psych out their opponent or just for the lulz.

Sometimes though one of the fighters will be genuinely complimentary to the other. Not in a sarcastic "Nice punch!" kind of way, but sincerely praising their opponent. It might be a disguised form of gloating ("You're awesome, and since I'm kicking your ass that makes me even more awesome") but the point is that they mean it.

Most common from the guy who is winning, since coming from the loser it might sound like they're making excuses for being beat. The praise will often stop when the tide turns, but some characters will keep it up all the way to their defeat.

When someone takes delight in the amount of destruction a fighter causes, that's In Love with Your Carnage. This is usually intended as a compliment but the object of the affection may or may not take it that way. Crosses over with Baddie Flattery when the fighter doing the compliment is also a villain. For an even more polite assailant, see Apologetic Attacker.

Contrast You Fight Like a Cow, where the characters battle is as much verbal as physical (though it may still be somewhat friendly).

Examples of Combat Compliment include:

Anime and Manga

In Samurai 7, when Kambei was fighting Kyuzo, he said "I'm in love...with your fighting style," or something like that.
Magical Girl Lyrical Nanoha A's - The rematch of Fate and Signum had both fighters pausing momentarily after a flurry of blows so that they can compliment the other's skills and the power of their Device.
- "You're young, but you're a good knight" were Zest's words to Vita in StrikerS when she was handily stopping him from achieving his goal. Agito promptly complained to Zest about how he shouldn't be wasting his time praising his opponent.
In Dragon Ball, when Goku fights Uub in GT. His entire purpose in the fight is to gauge Uub's strength, and he is pleasantly surprised.

Film

In the climactic fight in the Iron Man movie, Stark's opponent is constantly praising Tony's technical genius and tactical cunning.
In the famous duel in The Princess Bride both fighters treat the whole thing like a game and are free with their compliments of each other's skills. There are also some good-natured compliments between the Man in Black and Andre the Giant during their battle.
Star Wars: At the end of Empire Vader does it to Luke to try and encourage him to unleash his dark side, and then the Emperor does the same at the end of Jedi.

"Impressive. Most impressive. Obi-Wan has taught you well."

In Serenity, The Operative compliments his opponents accomplishments, but also declares their "sin".
Jack Sparrow complimenting Will's form during their first duel in Pirates of the Caribbean: The Curse of the Black Pearl
Star Trek VI: The Undiscovered Country - General Chang appreciates Kirk as a fellow warrior.
In The Mask of Zorro, when Captain Love was fighting Alejandro (Zorro), he compliments him by saying "you're doing well, your brother would've shot himself by now."

Video Games

Metal Gear Solid is full of this. The bosses in the game often compliment Snake's ability. The most pronounced is probably Snake and Ocelot in Metal Gear Solid 3—at the beginning, Snake defeats Ocelot but compliments his ricochet shots and in later battles, Ocelot compliments Snake for good shots.
All of the fighters at the Dojo in the first Paper Mario.
It's common courtesy in FPS's to compliment an opponent on a particularly good kill. Even/especially if the one killed was you.
In Mega Man 8, Sword Man's death quote is simply "Nice Shot."
Tokugawa Ieyasu praises his opponents in a friendly, chatty way as he punches the crap out of them and their armies in Sengoku Basara 3. Makes sense, since he's actually trying to recruit some of them into his army and dissuade others from the path they've chosen...by punching the crap out of them all.

Western Animation

In the Avatar: The Last Airbender episode "Sokka's Master", Sokka receives several compliments about using his environment and superior agility during an intense sword fight. (With an Old Master who's teaching him, mind you.)
Kim Possible - When Kim first wears her new Post Script Season mission garb, Shego admits that it looks pretty good (this after mercilessly—even by her standards—mocking the various outfits she'd worn earlier in the episode).