The scenes after the party gets split up after arriving to the Fallen Arm are full of these moments:
Shulk gives Fiora her first kiss and is so overjoyed that she's back and remembers him.
Sharla raises Reyn's spirits after he tells her of the confict he has for not being able to fulfill his promise of protecting Shulk. Soon enough he's back in action.
Specifically, Reyn says he's worried that Shulk doesn't need him anymore now that he has the Monado and gotten stronger than him. Not five minutes later, he and Sharla pull a Big Damn Heroes moment, backing Shulk up as he desperately tries to get the Monado working again to protect Fiora from a mechon patrol. Evidently, Shulk still needs his friends after all.
Dunban asks Melia how she's doing and she replies that she's fine, but Riki insists to make camp since he's tired and hungry. Gilligan Cut to the three around a campfire with Melia in a very deep sleep and Riki catching fish. Dunban quickly figures out that Riki knew just how tired Melia was even though she wouldn't admit it.
On that note, the entire conversation between Riki and Dunban right after that scene, the most unlikely Odd Friendship in the game. Being able to bond over their parenting experiences was d'awwww worthy, and the absolutely lovely music box rendition of Riki's theme that plays during that moment seals the deal.
And one more for Dunban, when he finally reunites with his sister.
For Melia, Kallian's death and the last thing he says to his sister. Also doubles as a Tear Jerker due to the beautifulmusic. And immediately afterward, Melia is almost unable to contain herself when she hugs Riki after he said he was the only other one to hear Kallian's parting words to her.
One of the highlights of these is the final one between Shulk and Riki, where Shulk laments how he doesn't have a family waiting for him back home after their adventure's over. Riki's immediate response? Tell Shulk if he wants him to be his daddypon and become part of his family.
Shulk: ...Wh-what was that, Riki?! Riki: Shulk can live with Riki and Oka, then Shulk have family waiting! Shulk never get sad again! Shulk: ... Riki: Shulk not like Riki's idea? Riki very, very sorry, Shulk. Riki only want to see Shulk happy... Shulk: No, it's not that... Thank you, Riki. Thank you so much. No one's ever asked me to be a part of their family... Riki: Shulk not worry anymore! Riki want to always see big Hom Hom smile from ear to ear! Shulk: (You are a great friend Riki...)
Restoring Colony 6 and sending more immigrants to live there brings warms feelings seeing all sorts of different species coming together.
Shulk and Fiora have unique dialogue when healing eachother in battle. Awww.
Fiora's final skill tree being entirely devoted to buffs she get from Shulk being in the party. It is all unique to her so you cannot link them with other party members. It is both kind of funny and super sweet.