I'll start out with something that's relatively simple, the Fire Emblem: Awakening fanfiction Matchmaker, where in Robin (The default female Avatar/My Unit) tries to pull off something you cannot replicate in-game and have the Lord Chrom pair off with Cordelia, the Pegasus Knight with an unrequited (and secret to Chrom) crush on her lord.
The main CMoH points would of course be the romantic confessions and stuff, but there's another moment that I think is really effective; Chapter Six takes place during that chapter of the game (if you've played it, you should know which one) and after a long series of terrible things happening, Cordelia is saved from certain doom by "Marth", Chrom's ally from earlier in the game. Cordelia manages to tell Marth a bit of her troubles, and Marth responds with a small pep-talk that's able to finally get Cordelia moving forward again.
Spoiler: show
So, what moments from fics made your hearts warm?