Any time Shizuku's face turns red is usually this.
The first time Shizuku skips class, and the revelations that come with it.
For a love story about two very, very, very anti-social people, it's heartwarming to see them declare their love so early. Haru decides he loves her midway through the first episode, and Shizuku decides she reciprocates at the end of episode two. Most love stories, especially chick flicks, are about the main couple actively denying their love as hard as they can and only get together at the very end, as if it were just a reward for getting through the movie. So the main couple falling in love because they're in love, and not because it's a reward for getting through the season's plot twists, is really sweet. They're both already in love, and neither denies it, and the rest of the season is spent figuring out what love is so they can both be more in love.
Shizuku's second love proposal, and the following discussion, was very sweet too.
The 'I know that you're a good person.' speech. This speech taking place after Haru beat the snot out of some punk, and around the corner from the human shaped bloodstain marking where he beat the blood out of some other punkier punk.
Then Haru tells Shizuku she's like a hero. And as Haru begins to stroke her bruise, they both blush red...
Haru: I thought you got mad and left.
Shizuku: Yeah, I did. [[Beat]] We have watermelons back at our place. Want to smash them?
Haru: You're always there to save me. I need to do something for you.
Shizuku: A date.
Shizuku: Take me on a date.
Shizuku making it clear to Haru that the fact he's a distraction is her fault not his.
Shizuku listening to Yamaken's advice during the festival. This is the first time she's ever listened to anybody else's opinions.
Natsume trying to give Shizuku advice. It failed spectacularly, but it was still endearing. And of course, Nii-chan comforting her afterwards.
Shizuku telling Haru TO HIS FACE that she's come to realize that she's acted stupid.
Then she finds him sleeping. Possibly trying to repay the gesture of romance he pulled when he found her sleeping in episode two, she tries to lightly touch his hair. Then when he wakes up, she opens up to him, tells him why she's been so cold lately, and asks him to wait for a while until she stops being confused.
Open hearing Shizuku's story about the empty goldfish pot, Haru immediately tries to catch a crawfish for her.
In a dark way, Haru threatening to kill Yamaken counts as this.
The whole 'spider's thread' conversation. "Your hair looks strong" will be the most romantic thing you've ever heard.
Until less then a minute later when you hear this: "I wanted to talk to you before the course started. I love you, Haru. So you don't need to worry. I've made up my mind. You can trust me, Haru." This after Shizuku thought 'It would be pointless to tell him he doesn't need to worry'. She tells him anyway.
The smiles on their faces. The dopiest frostbitten smiles!!
The very episode that Shizuku decides she and Haru are officially a couple, Haru becomes a green eyes monster. He attacks Yamaken behind her back, and goes so far as to ask her to stop going to cram school with him. There's even a visual of a spider's string snapping to symbolize how fed up she is with his behavior. But she makes it clear that they're still a couple, and tries to understand where he's coming from.
Shizuku and Haru having a sleepover, then watching the New Year's sun rise, completely unplanned.
Natsume's plans for the Kingdom of Mitty.
"This is fun. Let's do it again next year!" Smile.
Haru spent all day searching for a Firefly. Because he thought it was pretty, and he thought it would be prettier if he was watching it with Shizuku.