Surprised no one put this but Gilgamesh's response to Iskander asking him to join him in Episode 23 is an amazing CMOH, considering it's Gilgamesh.
Gilgamesh: "You never cease to amuse me, it's been ages since I laughed so hard at anyone but a fool. But unfortunately, I have had but one comrade, and he is all I shall ever have."
Following that, and his defeat of Iskander, Gilgamesh remains that he considers the King of Conquerors a worthy opponent.
Gilgamesh: Feel free to challenge me again as often as you like, King of Conquerors. This entire world, is my garden until the very end of time. Thus, I guarantee you this- it will never bore you. It will always be entertaining.
Iskander: ... That sounds very good.
Saber takes Iri for a walk in the city after the latter spent her entire life in a castle.
In the anime, that there's a whole episode dedicated to Rin is a CMOH in itself. The way she defends her friend Kotone from the bullies and then rescues her from Ryuunosuke is another.
The scenes used during the 2nd ED, showcasing the development of Irisviel and Kiritsugu's relationship status going from "Magus Killer and Homunculus" to "Loving Husband and Wife" definitely counts as one.
And in case you missed it, the scene in the ED of the two of them going through the forest together is made to look at first like they're walking into the light.
Waver using all his command spells to release Rider from his servitude. Rider refuses to leave and Waver breaks down in tears.
Rider: "Even if you are not my master, you are still my friend."
In Episode 22 of the anime, Waver's conversation at dawn (after having spent the entire night walking back into Fuyuki City after Saber destroyed the Gordius Wheel) with Glen Mackenzie on the roof of their house where Glen reveals he's aware Waver isn't really their grandson, but he's made the elderly couple so happy (they don't see their real grandkids anymore) that Glen asks him to stick around.
And afterwards, he does stick around.
It's even more touching when you notice how very similar grandpa looks to Alexander.
Episode 25: Kiritsugu finding a young Shirou in the midst of the fire. Shirou's narration notes that it's more like Kiritsugu is the one being saved rather than Shirou. For a moment, all he can say is "He's alive", sounding just so relieved. The final scene of the series is one well-known to the fans of Fate/stay night — Shirou and Kiritsugu sitting outside on a moonlit night. Kiritsugu tells Shirou how he failed to be a hero and Shirou resolves to be the hero the adult Kiritsugu can no longer be. Kiritsugu smiles and comments that "Now I can be at peace." He dies right after that.
Even better, the narration during the moment when Kiritsugu finds Shirou is taken straight out of the flashbacks in the Fate/stay night visual novel. It's all the more powerful after Kiritsugu has come to believe that his life was a waste based on a lie that destroyed everything else he loved for nothing. At least he does some genuine good.
It's paired with the sun breaking through the clouds above Saber, as if to reassure the viewer that everything will be okay in the end.
Unless you remember her fate in the Heaven's Feel route.
In the same episode: Kariya is finally taking Sakura home. Aoi turns out to be alive. The Tohsaka sisters are shown accepting him as their father. What can possibly ruin this beautiful scene? The immense Tear Jerker right after it's shown that it's just Kariya's dying vision.
Saber showing a sense of pity towards Kiritsugu after the underhanded way he dealt with Kayneth. Despite her anger towards his actions, she's far from harsh when she answers Kiritsugu's War Is Hell speech and is able to see that there was once a person who believed in righteousness.
Tokiomi's last scene with Rin and Aoi struck a chord in me for some reason. It's the closest we'll ever get to seeing the Tohsakas happy.
if you're counting out of character moments, the ending of the Einzbern Consultation Room series and it's sudden turn towards a fully self-absorbed ending. Especially the last words between the Grail's Lawyer and Student Number Zero, which makes the normally annoying, depressing, and occasionally funny Tiger Dojo segments of FSN suddenly heartwarming. Zero-chan kept her promise to become an instructor who corrects bad ends and is kind to Illya... In her own way.