The series sometimes takes the Foe Yay between Masamune and Yukimura to ridiculous heights. After their first fight Yukimura was left literally weak in the knees, they're always so into their matches, they spend the majority of the show thinking about fighting each other and Sasuke even comments that they might have "fallen" for each other from their first fight. In episode 10, when Masamune went to grab Yukimura's necklace, half the fangirls/fanboys were expecting him to just kiss Yukimura there and then, genre be damned.
And in the second season the necklace-grabbing scene turns up in both of their flashbacks about each other, while Yukimura fanboys Masamune and Masamune speaks fondly about Yukimura being "pure" and "out of this world, no kidding" and "so fiery I can't get away with only a burn"...
The handshake scene from the second OVA competes with the necklace grabbing one in terms of sheer Ho Yay, a CM for the movie has Masamune declaring that Yukimura is the only one who can really heat him up, and in an article about the movie we have the director emphasizing that Yukimura is the most important to Masamune.
Kazuya Nakai said their battle in the movie was referred to as a love scene. Make of that what you will.
To which Tohru Ookawa remarked that Ieyasu and Mitsunari were no less passionate about each other...
Yukimura: My heart is burning. Such presence. Such fighting spirit. Such... strength.
Sasuke: Er, please don't tell me he lit your soul on fire.
It's even more obvious (and lampshaded by Sasuke) in a later episode when Yukimura and Masamune reflect on how badly they want to fight each other.
Yukimura: The one I really want to fight is Date Masamune, the One-Eyed Dragon!
Sasuke: You really fell for each other...
In the second season they fanboy each other in what can only be described as daydreams. In the last episode Masamune even seems to sense when Yukimura goes down.
You know you've got serious Foe Yay in your anime/game series when even the T-Shirts come off as slashy.
Masamune and Yukimura sit on the fence between Foe Yay and simple Ho Yay, because while they are enemies who will one day probably fight to the death, they actually like each other, enjoy fighting each other, and outside the battlefield they get along pretty well.