When Emma finds out that Mr Elton was not, and had never been, interested in Harriet she does "acknowledge herself grossly mistaken and misjudging in all her ideas on one subject, all her observations, all her convictions, all her prophecies for the last six weeks" (17). She is not too proud to admit that she has made a mistake, and she does what she can to cheer up Harriet and make her feel better.

"She got her to Hartfield, and showed her the most unvarying kindness, striving to occupy and amuse her, and by books and conversation to drive Mr Elton from her thoughts." (17)

Emma does repent her match-making scheme and is very sorry that she has been the means of causing Harriet pain. I also think this quote:
"Such a blow for Harriet - that was the worst of all. Every part of it brought pain and humiliation of some sort or other; but, compared with the evil to Harriet, all was light; and she would gladly have submitted to feel yet more mistaken - more in error - more disgraced by misjudgement than she actually was, could the effects of her blunders have been confined to herself." (16)
shows that there is a lot more to Emma than a snobbish, class-conscious girl with too much spare time on her hands. She has a good heart, she is compassionate, and she wants the best for those around her. She is also able to put others' needs before her own which is not a bad quality.