When the hero and the villain clash repeatedly, over time they may develop respect for their opponent's abilities. After all, their adversary is able to keep rising to oppose them battle after battle. In the heat of battle the hero or villain's true capabilities and determination could be revealed. Or perhaps one of them was simply looking for a challenge. For whatever reason, the battles have created a sense of respect (which may or may not be mutual).
This leads to a declaration by one of the two that they have found their adversary a worthy challenge, or some variation of that. It can be privately said or publicly admitted; what matters is that the character in question acknowledges and respects their opponent for their skill. Should one side actually come out on top or find out the other has fallen, it may lead to Sympathy for the Devil, Sympathy for the Hero, or an Antagonist in Mourning.
This declaration is more commonly made by villains than heroes, given that the villain's less scrupulous nature doesn't exactly help earn a hero's respect. The exceptions to this tend to involve Spirited Competitors or otherwise less principled characters on the heroic side, or a Noble Demon on the villainous side. Compare Evil Virtues, wherein the heroes may recognize some admirable quality in an otherwise-villainous character.
Expect to hear Combat Compliments. A character who thinks this way is likely to have Faith in the Foe. This can lead to The Only One Allowed to Defeat You, depending on the mindset of the character making this statement. See also Friendly Enemy and Evil Counterpart. Can overlap with Enemies Equals Greatness. The idea of this trope is deliberately designed to sail over the head of the Arrogant Kung-Fu Guy as they can only think about beating their foes and being the best with zero regard for the battle itself (the realization that, yes, you can respect your opponent/the battle you shared and still be a great fighter is the key turning point in their Character Development). This is very common with a Mirror Character.
Worthy Opponent has been suggested to play 2 roles. Click below to see other actors suggested for each role, and vote for who you think would play the role best.