Mr. Knightley, when he offers to dance with Harriet after she is snubbed by the pompous and mean-spirited Mr. Elton. Even more awesome since she regards this as more exciting and memorable than being rescued from very scary gypsies by Frank Churchill.
Mr. Knightley when he admits his own faults during his proposal to Emma and says he loves her, believing her "faultless in spite of her faults" and that she has borne his rather frequent lectures "as no other woman in England would have".
Emma herself in her epic, chapter-long epiphany near the end of the novel, in which she not only realizes how wrongly she has thought and acted, but also that she is in love with Mr. Knightley. That level of intelligent self analysis by a spoiled child is really impressive — all the more so as she directly decides to do the right thing instead of scheming to supplant her rivals.
Emma's post-Box Hill thoughts and actions are also highly awesome. She genuinely regrets what she did and she knows how to make amends.
Emma's brilliant answer to Harriet who wonders why Emma, charming as she is, is not married yet. Why, Emma would have to find other people charming and be charmed by them!