Anything that shows Shovel Knight and Shield Knight together is either adorable or tear jerk-ish.
An easy to forget one goes to the Order of No Quarter near the ending: Being defeated by Shovel Knight in succession, they are left holding on to each other in a Chain of People; they hold each other, especially members who are falling after being defeated, and don't let go no matter what.
After the first phase of the Final Boss, Shovel Knight can hold Shield Knight who is falling down to the ground just like in his dreams, Shield Knight's reaction cements the heartwarming feeling.
Shield Knight: ...You caught me. Shovel Knight: If only I had known, I would have come sooner! Shield Knight: You knew I was still there, even though it seemed hopeless, you never gave up on me! Shovel Knight: I will NEVER give up on you. I will follow you to the end of the world. Shield Knight: It appears that maybe you have.
There's something about seeing all of the Wandering Travelers ready to fight together in the credits sequence that's just heartwarming. Especially The Baz, seeing as he finally got what he wanted: an order of his own to join.
The final battle, in which the player has to work together with Shield Knight to defeat the boss. The only way to reach the boss's weak point is by bouncing off her shield, and one screen-filling attack can only be evaded by hiding behind Shield Knight. It's heartwarming getting to see in gameplay how these two work together.
Special mention to the ending. Where Shield Knight is revealed to have survived, limps all the way to Shovel Knight's camp from presumably the Tower of Fate, sees that he is resting, and just lays down to rest beside him.
Plague of Shadows
Damn near everything involving Plague Knight and Mona.
After defeating King and Specter Knight, Plague Knight returns to his hideout and finds Mona dancing alone... His awkward reactions and answers when Mona tells she has no one to dance with sells the whole thing. The heartwarming goes Up to Eleven in the ending, showing Plague Knight waltzing with Mona using the skills he leaned from the Troupple King.
After defeating Shovel, Mole, and Treasure Knight, Mona clearly pretends that the level to their machine is jammed, wanting Plague Knight to "help" her. Plague Knight goes over to her, placing his hands over hers (as noted by text)... and then the lights go out, followed by Percy being a Moment Killer.
After conquering the Armor Outpost, buying the Trouple Chalice and learning to dance from the Trouple King. If you try to practice at the Potionarium in front of Mona, Plague Knight just stands there poking his forefingers together.
The entire reason Plague Knight wanted to create the Ultimate Potion: To become strong enough so Mona would love him, unaware that she already did. Crosses into a bit of a Tear Jerker if the player encounters Black Knight on the map, which has Mona run off and not appear for the rest of the game. Plague Knight clearly misses her, not even happy (at first) when he collects all 8 essences. Comes to a head in the endgame where, after defeating the Corrupted Essence and regaining the Ultimate Potion, Plague Knight discards it, allowing its energy to blow up the Tower of Fate, claiming that since Mona loves him, he has everything he'd ever need.
A few ending scenes showing the newly hooked-up couple enjoying their relationship, including having a romantic dinner on the Flying Machine (with Propeller Knight as the waiter), and later on, coming together in the best way they know: SCIENCE!
After defeating The Baz, Plague Knight can hire him as one of his minions. Once hired, The Baz shows an incredible amount of loyalty. It really shows how much he just wants to belong.