Magical Girl Lyrical Nanoha StrikerS/Heartwarming

Teana's "I'm sorry, I'm sorry, I'm sorry..." as she sobs in Nanoha's arms after falsely believing that she held her back out of fear she'd surpass her, then discovering that Nanoha's real motivation was to protect her from the same hideous injuries that have befallen Nanoha herself due to constant overstraining and that Nanoha had long arranged her training in the very same direction she wanted to go herself, if only she had a bit more patience. Seriously, what can be cuter than a die-hard Tsundere in a situation like this?
Almost every scene with Vivio. She's just that adorable.
- The morning Nanoha wakes up and notices Vivio sleeping next to her on the bed that Nanoha and Fate share. She gets up to get ready for work, and Vivio starts whimpering in her sleep when she notices that Nanoha is no longer next to her. Nanoha then picks Vivio up and places her next to a sleeping Fate. Fate then, without waking up, turns and holds Vivio. Nanoha then smiles and leaves for work.
- In one episode, Nanoha encourages Vivio to stand up on her own after she trips over. In the finale, after Nanoha and Vivio have been forced to fight each other, culminating in Nanoha hitting Vivio with her strongest possible non-lethal attack, the reverted-to-normal Vivio is collapsed in the resulting crater and Nanoha tries to approach her, only for Vivio to tell her to stay back. It's a heartbreaking moment, until she continues, "I... I can stand on my own." and Nanoha realises that, instead of being afraid of her, Vivio is trying to make her Mama proud of her.
- Vivio is clinging to Nanoha, who is telling her she'll be her mama. Fate intervenes, and notes that she's also her mama, in a way. Vivio, of course, looks pretty confused, as, like most kids, she seems to believe one should have one mama and one papa. She starts almost crying in confusion, and calls out, "Mama?" to which both Nanoha and Fate answer back, in perfect unison and the sweetest tone imaginable, "Yes?" Vivio finally gets it, smiles with still-misty eyes, and hugs them both.
- Vivio, in tears, tells Nanoha that she's not a real person, that Nanoha and Fate aren't her real mothers and that she deserves to die because she's a Person of Mass Destruction who only had one purpose, which was powering up a massive warship. Nanoha shakes her head and tells her that no matter how Vivio was born, she's still the little girl that Nanoha had been taking care of and the girl in front of her wasn't fake or a monster or anything like that. Nanoha then asks Vivio what she truly wanted.

Vivio: Mama... Save me!

When Fate has been paralysed by Scaglietti's Hannibal Lecture about how she's treating Erio and Caro just like her mother treated her, Erio and Caro counter by giving a You Are Not Alone speech about how much they love Fate for all the things she's done for them.
Hayate embracing the badly wounded Vita in episode 25. "There's nothing in the world... that they can't destroy."
After Signum and Agito enter Unison in the end. "Agito, I feel warm when in Unison with you..." Agito doesn't answer because she is too busy wiping off sudden Tears of Joy.
The manga shows how Fate met Erio, after saving him from an unethical research institute. Discarded by his parents and realizing his existence was fabricated, Erio violently lashed out at anyone who got close. Fate pays him a visit, and tries to talk with him.

Fate: Erio, you can't just flare up at people like that...
Erio: SHUT UP! THIS HAS NOTHING TO DO WITH YOU!
Fate: It does. I want you to be happy. And I've come to take you from here.
Erio: NO ONE ASKED YOU TO DO THAT! TO YOU, I'M NOTHING! NOTHING AT ALL!
Fate: You aren't nothing, I-
Erio: *blasts Fate with electricity* DON'T TOUCH ME!
Fate: *gently holds Erio despite burns on her hands* See, Erio. Right now, you're full of unhappy feelings, and thoughts of unforgivable things. I certainly wouldn't be able to understand all of it. But I want to try and understand at least a little. I think we can share some of our unhappiness. I was the same as you, Erio. Told I was unneeded by the person I loved. Told I was a failure. It was painful, and lonely. I felt like dying. But, unhappiness doesn't last forever. Fun things, happy things, if you look, you will certainly find them. I'll help you search. So please, don't hurt others in your sadness.

The scenes of Zest, Lutecia, and Agito in the third Sound Stage. The fifth track in particular, which begins with Lutecia being adamant about reaching the next town before lunch for the sake of Agito even though she was dead tired, leading to Zest giving her a piggyback ride so she can sleep on his back while he carries the both of them there. It's just a sweet scene that shows how much the three of them care for one another, which also makes this a bit of a Tear Jerker if you listened to it after StrikerS.
Toward the end of Episode 13, there's a nice friendship moment between Hayate, Nanoha and Fate.

Hayate: To me, you’re the people who saved my life and my beloved friends. I don’t know what will happen to Section Six, but…
Fate: You already told us that when we joined. Both Nanoha and I chose to be here knowing that. It’s okay.
Nanoha: Besides, getting me into the instructors’ squad and setting up Fate-chan’s examinations were things you and your whole family was instrumental in.
Fate: So now we need to help you achieve your dreams.
Hayate: That’s no good, we’ll keep helping each other forever.
Fate: That’s what friends are for.
Nanoha: (salutes) Commander Yagami, I don’t think that you’re doing anything wrong right now.
Fate: (salutes) So it’s okay. Give us your orders like always with pride in your heart.