The whimsical and innocently romantic lyrics of Save My Heart wonderfully summarizes Touka's new-found hope in life that Shidou has given her:
My life was monochrome and colorless, until the day you appeared, and then the cold cold winds stopped blowing. With every sincere word you say, new meaning poured forth endlessly; what do they mean? You are so different from everyone I've met to this day, I want to know if you stole my heart? Feel Me: Maybe you are the only one, who can wake me up from my eternal sleep Like the Gallant Prince in storybooks from childhood. Touch Me: I know have a feeling that only you, Can open that eternaly locked door With your hands gently turn the key Please, Save My Heart.
Since a heartwarming moment is practically a prerequisite for getting each Spirit to trust Shido enough for him to seal their powers (with the exception of Kotori, who already was, and still is, at a maximum affection level with Shido), of course we'll have quite a bit of these over the series. The heartwarming moment for each volume that results in the sealing of a Spirit's powers:
Volume 2: Shido crosses a five metre barrier of blizzard (which could easily have killed him or frozen him) that Yoshino set up just to get to her to hand her Yoshinon, which he finally managed to find. He makes it to her, barely alive, handing her the puppet. Cue Cry Cute moment from Yoshino.
Volume 5: When Shido finally manages to convince the Yamai twins, who were fighting each other trying to wear themselves out enough for the other to kill her so the other can live on as Yamai, that as much as they care about each other, deep down they really don't want to die either, and that they really actually want to continue to live together. The duo finally make peace and stop fighting due to this.
Another one would be that Kotori, despite abusing Kyouhei because of his masochistic tendencies, places her belief in him that he will save the Ratatoskr crew (as she wasn't in the ship at that point) from an attack by DEM.
Volume 7: When Shido makes good on the promise he made to Miku to save her if she were ever in danger, in response to the question she asked on a whim, and didn't expect him to keep, given that she had lost trust in humanity, especially guys in particular. In addition, she didn't expect to be protected or even thought of by anyone (least not a guy) when she lost her voice (which had happened when she ran out of spiritual power there and then), which was the only thing going for her, and without which she would be worthless. Granted, he already resolved to save all spirits no matter what (including Tohka, who had given in to her Superpowered Evil Side and was the one the two of them were fighting in the first place, and Shido didn't want her to kill anyone either), but it still counts as theheartwarming moment for this series so far.
While Ai, Mai, and Mii normally mock and berate Shido, not even mind control can force them to say Shido doesn't love Tohka.
Volume 9: After everything that Shido and his friends have been through from Natsumi's antics, Natsumi still in denial and believes it's a ruse. However when she escaped by transforming herself into Kotori using her powers, she learns the truth that they do care for her even Shido consider Natsumi's tricks as a minor problem considering on how he been through in the past volumes. This causes Natsumi to be crying in tears as she was the one who's wrong about them and realizes her error. In the end, she manage to make peace and apologize to Shido and his friends for everything she has done.
Volume 11: All of it. Even add in as a Tear Jerker moment in the series as well.
In the first timeloop, Shido manages to comfort Past!Origami after losing her parents, which is when Shido realizes the truth on how Origami knew him from the beginning yet didn't recognize her himself. After learning the truth, Shido decides to go back into time again with the help from Past!Kurumi and saves Origami's parents.
It turns out that the Origami in the old timeline didn't actually love Shiro but someone to rely on to cover up her own weakness. However once both memories have been merge and her spirit powers have been sealed, Origami decides that the real love for Shido starts now.