Joe, after discreetly noticing the jealous Lilly mocking Mia's new hairdo/makeover, asks her privately about her tears, then reminds her:
Joe: No one can make you feel inferior without your consent.
Mia: Eleanor Roosevelt said that.
Joe: Another special lady, like yourself.
At a state dinner, her first public appearance, Mia takes too much sorbet, gets an ice cream headache, and begins to flail wildly. The guests next to her (one of whom is the prime minister!) realize what is going on and give themselves ice cream headaches to take the spotlight off Mia.
Lilly's heartfelt speech to Mia to try and convince her to be a princess.
Mia's letter from her father.
"Because you saw me when I was invisible."
After a botched routine surgery on Julie Andrews' vocal cords tragically robbed her of her amazing vocal range, it seemed that Andrews would never sing again. But The Princess Diaries 2: Royal Engagement changed all that, when she was given "Your Crowning Glory", a song deliberately written as easy for Andrews to sing. Hearing her in a Disney film singing this simple, yet beautiful song and gaining the confidence to sing in public once more certainly qualifies this as a CMOH.
The scene with the girls from the orphanage in the second film definitely counts.
The ending of the second movie where "the sparrow takes off" and "the eagle flies for the last time". Not only is it awesome to see Mia finally crowned as queen, but almost everyone from throughout the movie, even those who had seemingly been against her or at least to enjoy her misfortunes are all there and happily join in on the Genovian national anthem, from Nicholas and the stoic new secret service agent, to her ex-fiance and his love interest, to the annoying Scottish gossip-rag journalist, even the scheming nobles from the first movie—and a song that was mostly Played for Laughs in the first movie becomes a sincere, heartfelt, even stirring performance.