After Shi starts listening to Hibiki, they're always cute together. The best part's when they rush into each other's arms near the end of the first book.
Yukko spent years researching how to make a human form homunculus, to replace the daughter she'd lost. Once Hibiki selflessly tries to give her Shiraasan as her daughters replacement, Yukko is touched and is finally able to accept her daughter's death and move on. But the best part? It turns out Yukko had sacrificed her ability to dream while she slept for her magic. Once she let go of her grief, she was finally able to dream again.
When Ahito wakes from his defeat, he finds Hibiki at his bedside. She'd stayed by his side until she was sure he was okay. She even cried over his Dark and Troubled Past.
Hibiki offers some of her soul to help a demon. The act in itself seems to have been enough to help.
The old man's story about his son, which he tells to a friendly demon. His son was gentle and loved flowers, and to have such a son vexed the old man, but he dearly loved him. One day, his son went off to war and never returned. He asks the demon that, should she find him, to tell him the war is over and he can come home.
Yukko created many homonculi to try and bring her dead daughter back to life, but they all ended up as blobs of jelly which fell apart after one day. In the end, her daughter's magic tears are used in a potion to save Shi-chan.
The conclusion to the three-parter with Setsuna. From the meeting between Shirotsuki and Ahito where Shirotsuki says that though he doesn't remember who Hibiki is he still feels as though she's family to him, to Ahito's Manly Tears when he sees that he saved Hibiki's life, to Hibiki thanking him for it even though he claims that it was Shirotsuki's doing, to him telling Setsuna about Mizuki and how he was afraid that she might be an apparition of Mizuki come back to haunt him, only for Setsuna to respond that if she truly were Mizuki's ghost, she'd have been there to thank him... The entire chapter is just one big Crowning Moment of Heartwarming.
In the birthday chapter, when Hibiki thinks back on how she forgot her true birthday. The date she gave everyone else was simply a fake. Cue a shower of presents from her friends once the word spreads that her "birthday" was yesterday!