TL;CR

TL;CR MEME
1. Comment with your character.
2. Receive comments from others.
3. Reply to their comments with long ballads and explanations of your characters' relationship throughout the game.
4. Endure everyone else reading your comment like the vultures they are.
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Even from just their first few threads, she thought she was a pretty nice kid who she didn't really have any objections to. Emma is... pretty judgmental even though she tried to hold some of that back during this game in order to get along with people easier, so it's definitely worth noting that she never once thought Miki was acting weird or doing something stupid or annoying.
I think the first thing that really moved them past 'oh she's a nice kid' territory was Miki using her scroll to find out that Xion killed Hisoka. In the first place, she was pretty proud of her for that, and that pride only really increased after she found out later how difficult it was for her and how much she struggled with the decision both before and after. Doing something that you think will help people even though you're scared or don't necessarily want to see the outcome it brings is definitely worthy of respect in her book!! But following Miki confiding those worries, Emma absolutely started caring more for her and wanting her to do well, because she could relate really well to the worries and fears she was describing. By that point, she was also starting to see how much Miki was trying for all the people around her, too.
And then they got to boggart week, and that care and respect Escalated Even More. We've talked about it before, but their experiences (while different!) definitely struck a chord with each other enough that Emma was able to relate to the things she had been through pretty easily. I think the talk they had about what they had both experienced afterwards really cemented it for her - while she felt a little bit awful about it, because nobody (especially someone as young as Miki) should have to go through something so terrible, and she'd definitely change it if she had that power... It was a little bit of a relief to have someone who understood in a way no one else could how awful it is to have to fight against people who you recognize and may have been close to once.
That got solidified even further when they had Boy Talk, because even though Axel and Kaoru are obviously very different people, most of what Emma and Miki talked about was how they each of them made them feel like there was something to be happy and hopeful about after having been through something so traumatic and bleak. That, and how she talked about being exasperated by what happened in the CYOA and having to look after people, in addition to how she leapt right into helping Axel after he got hurt in the trial, made her think that her and Miki were fairly similar people. Being constantly ready to help but also being exhausted by having to look after people who should know better is a Big Emma Mood. Because of that, she was probably going to tell Miki about her role before too long, but then Miki died just before they could get to that point.
After that happened and she found out about Miki's role, she was... Hurt isn't the right word, because she definitely understood why she wouldn't want to spread a secret like that around (and it's not like Emma had told her about her role at that point), but definitely sad. Once she heard that even Shess didn't know, her main concern was whether Miki had someone to share that burden with other than Four. She wasn't really angry about whatever might have happened over the course of her role, because she understood the importance of making sure the corrupted couldn't hurt anyone else, but she was definitely worried about the toll it might have taken on her.
Overall, she definitely thinks Miki is a very smart, strong, and kind person!! And she hopes they can keep in touch after all this is over.