For This Troper, the CMOH in Final Fantasy XII: Revenant Wings was when the group had been transported to the home of the Yarhi, the realm of Illusion, and everyone's looking for Vaan (who'd faded away) in The Neverwood. Even though Vaan's there (although transparent) everyone's left except Penelo, who speaks to Vaan, even though she thinks he isn't there.
Penelo: Vaan...can you hear me? I know you've got your doubts about Balthier, the Judge of Wings, the aegyl...well, everything, but you don't have to face those doubts alone. Ever since we met, you haven't done anything but get me in trouble. So if that's what you're worried about, don't. I'm used to it. I've never told you this, but sometimes, when we're flying, I get scared. But it never lasts, because I know you're with me. But without you...I could never fly.
Vayne: [wounded and dying] Venat! I have failed us both. I am no Dynast-King. You must find another. One who might realise your ambitions.
Venat: They are fulfilled beyond your knowing. The Cryst is sundered, Age of Stones complete. From the Undying Ones the world is freed. You shall not tread this path alone. Together we go. Come.
Vayne: Heh. Won't Cid be eager to learn what has happened here. History begins anew.
Vayne and Venat then merge together to fight (and probably die) together.
The 'moment' between Balthier and Fran at the top of the Pharos when Fran has been befuddled by the Mist after the Sun Cryst goes crazy. Fran implores Balthier to leave her behind, but Balthier refuses. Beautiful.
Fran: * lying in Balthier's arms* The Sun-Cryst bursts. You must run, as far as you can.
Balthier: Easy, Fran.
Fran: * Reaches up to touch his cheek* Hadn't you best be off? That's what a sky pirate does, you fly, don't you?
Balthier: * Takes Fran's hand, and smiles* I suppose you better hang on then.
The saddest/most heartwarming part is that 'hadn't you best be off?' was Cid, Balthier's father's last words to his son, before his death barely a minute before this moment. Balthier's expression says it all. In fact, Cid's remarks to his son as he dies are also prime heartwarming material. See the second half of this video.
Despite Larsa's position as Emperor of Archadia at the end of the game and their vast differences in social class, it's shown that he still communicates with Penelo through letters and eagerly anticipates a future visit from her. After losing almost everyone in his life, it's really nice to see that Larsa's friendship with Penelo is still going strong and serves as a source of happiness for him.
Just before the last boss, when Venat basically tells Vayne: "I am proud of you, and I forsake my immortality this instant so you do not have to die alone."
One of Clan Centurio's toughest hunters, a large bangaa named Monid, is always shown in the clan hall speaking with a little hume boy. As it turns out, that young boy is the orphaned child of Monid's deceased friends, who were killed while hunting the Trickster mark in the Paramina Rift. Monid now takes care of the boy and is raising him as his own adoptive child.
He also fights alongside the main party during the Trickster hunt. All to avenge his fallen friends and bring some closure for their orphaned son.
The little boy is always at the hall, even when Monid is out on a hunt, so it's likely that the rest of Clan Centurio watches over the child when his adoptive guardian is out doing his job, too.
At Jahara, Ashe is contemplating what to do about the nethicite when she sees Rassler's spirt again and runs towards it before then running into Vaan. For the first time ever, the two have an honest to god talk about their fears, their pasts, and why Vaan decided to come along. He was frightened that he would begin to feel hollow and alone, simply wallowing in self-pity as his talk about being a sky pirate was something he knew he honestly could never achieve and he used it to keep his mind off his brother. He then tells Ashe that he knows he'll find his purpose in life if he follows her, leading Ashe to say "I wish I knew", but Vaan reaffirms that he'll find them. To many people, the scene may not be heartwarming, but simply the two characters treating one another as equals when Ashe had previously treated Vaan like shit and Vaan's complete trust in Ashe even when she is in doubt is something amazing.
In the same vein, atop the Pharos, Vaan tells Ashe (interrupting her speech) that he knows she's going to destroy the nethicite, she responds back softly "Don't interrupt Vaan", which doesn't seem like much, right? However, "don't interrupt" had been Ashe's catchphrase for most of the early game, usually said scathingly to Vaan or the other party members. But this time, she sounds nostalgic and happy, if a little bit sad. It highlightes just how far Ashe had come and how well those two now know one another.
There's a little one when you take the Wyvern Lord mark. The person who hires you turns out to be one of those good-for-nothing-Archadian-imperialist-scum-soldiers that have been occupying Rabanastre. However, the soldier hiring you explains that he saw the dragon while on patrol, but his peers and superiors thought that if it attacked the town, they'd take care of it then. The soldier, fearing for the civilian casualties that would result and believing them to be inevitable, pays out of his own pocket for the dragon to be put down. It soon becomes clear that this goes well beyond Even Evil Has Standards; he as a law enforcement officer cares for Rabanastre and its people, and isn't just one of the generic Faceless Goons.
It's the last bit of dialogue before the hunt starts proper that's truly heartwarming: "This has naught to do with the Empire. I want you to hunt this Wyvern Lord for me!" You can't help but smile and think to yourself: "Alright, sure."
Vaan and Penelo's reaction to Balthier and Fran reclaiming the Strahl at the end. Penelo jumps on Vaan and forces him to give her a piggyback ride.
Bonus points for Balthier's note, which includes Ashe's wedding ring and asks Vaan and Penelo to return it for him.