When Elaine sees Guybrush in Spinner Cay in Chapter 2, she comes downstairs from the Royal Chamber and hugs him for a bit.
In Chapter 3, when Elaine accidentally scares the Monkeys of Montevideo in her Poxed state in front of LeChuck, she realizes her mistake and apologizes to them, then (in pretense) tells LeChuck, "Look at you, going out of your way to set things right. Who ever thought LeChuck would do such a thing?" He responds with, "It's only the beginning," before she wraps her arm on his shoulder... in front of the playful monkeys. This scene may also count as a Funny Moment.
The scene near the end of Chapter 3, when Guybrush and Morgan watch the manatees swim away from the Screaming Narwhal on both sides in a beautiful sunset, and at once he smiles... right before Morgan knocks him out unconscious. Oh well, it was a Heartwarming Moment while it lasted.
The Mêlée à Trois at the beginning of Chapter 5 with Morgan and Pirate Bill the Swordfighter. Guybrush tries to cheer her up by starting an insult swordfight. The Swordfighter is using good old insults from the previous games ("I once owned a dog that was smarter than you!"), Morgan is insulting herself ("It's hopeless. I can't believe I once studied under the greatest swordsman in the Caribbean.") and Guybrush uses the correct reply for the Swordfighter while complimenting Morgan at the same time ("He must've taught you everything you know.") This ends in a Moment Of Awesome where Morgan finally finds some fighting in her and defeats Pirate Bill in a single stroke. After seeing how Guybrush treated her in Chapter 4, it's heartwarming to see him trying to cheer her up.
The end of Chapter 5, in a reunion scene with Elaine and the newly-reborn Guybrush, when she tells him that, "After all these years and all of our adventures, two things are certain: that I always have a plan, and that Guybrush Threepwood will always come for me when I need him most." In response, regardless of any final topic you choose, he places her wedding ring back on her finger as they both smile at each other. Awwwww...