Seliph's conversation with the ghost of his parents after killing Arvis, especially with the remixed version of Seliph's theme.
Claude's conversation with Sylvia in chapter 4:
Sylvia: Ohhh! I bet your sister is real elegant an' beautiful an' all. Nothin' like me.
Claude: That's not true! I find you very attractive, and you have a grace all of your own.
Claude: Of course. I'd never tell a lie.
Sylvia: Wow! No one's ever said anythin' so nice to me! Er.. I feel funny inside... You are... so kind!
Sylvia's lover convo with Levin is quite heartwarming as well, questionable patch translation nonwithstanding. And then there's Levin's talk with Leen in chapter 10...
Arden's lover convos with Ayra and Fury are ridiculously sweet.
Also Lex and Tiltyu's convo. "Look, we've both been dealt a crappy hand. I wish we could've been together longer. I will cherish every single moment we had."
Adean's convo with Azel in chapter 4 can bring a person to tears of joy when you consider this is not only Azel's dream come true, but that she tells him just how happy she is to be with him.
Her convo with Midayle is just as sweet, for the same reason plus the element of devoted Bodyguard Crush.
Alvis telling Sigurd how much Azel means to him in chapter 1 of the game is heartwarming enough, but the Oosawa manga takes it Up to Eleven. During the wrap-up of the Verdane arc, Alvis actually talks to Azel in person and tells him he loves him.
Alvis: If by chance, some time in the future...no matter what happens, I always want you to believe in this fact.
Levin telling Fury he loves her in chapter 4.
Fury: Ah, so you and her were... I'm sorry. I didn't know.
Levin: Fury! You've got it all wrong. When I was a little kid I thought your sister was hot. But that was then. Now it's you.
Levin: I love you, Fury...
In the Oosawa manga, Levin is knocked out cold by a Sleep Staff and Sylvia risks her life to rush to his aid, telling the Bishop how wonderful he is as she holds him in her arms. Sylvia's feelings for Levin in general double as this and Tear Jerker material; the manga takes game!Sylvia's huge crush on him and adds a heartbreaking reasonwhyshe clings to him so. Makes it all the sadder that she doesn't end up with him in this manga.
And as a call-back, in chapter 34 of the manga she and Fury interact again after Sylvia's Tear Jerker of an explanation of her and Levin's bond... and not only they get along much better than the last time, but they smile to each other and promise to be friends. A very sweet and refreshing subversion of the usual catfights over a guy in the middle of a Love Triangle.
Azel's talk with Talito in chapter 4 of the game displays their bond of childhood friendship beautifully, and strengthens their Relationship Values at the same time.
This is expanded really sweetly in the Oosawa Mitsuki manga, where Azel reveals about how he constantly held Tailto's hand just so she won't cry on her grandma's funeral, and that's... exactly what happened. And on remembering that, this exchange happens:
Tailto: You have no idea, did you? Ever since that time, I've always liked you!! Yet, all you talked about was about Lady Adean...
Azel: .... Y-you're now going to say "Gotcha, Bratzel!" now, right?? (She's going to trick me, right?) Besides, you already have Father Claud!
Tailto: *blush* I do like Father Claud. But... it's different from the way I liked you...
The same holding hands eventually happened, on Adean's wedding with Jamke, but this time Tailto ended up crying anyway, but everyone ended up reassuring that it's Tears of Joy on the happy couple and realizing that she loved Azel. Sweet.
Some What Could Have Beenscenarios also add up some heartwarming moments, but the stuffs given about Azel/Tailto and Claud/Sylvia together were stuffs that may have warmed your heart, should it come true:
First off, Sylvia and Claud didn't die after the Belhalla, as much as Claud prophesized it. They reunited sometime after leaving Leen and Corple in the orphanage, but Claud has been paralyzed and blinded for life. Sylvia stayed with him regardless, tended to Claud and from afar, watched their children. Sylvia finally reunited with her children two years after Seliph's victory, although Claud has finally passed away in peace, more to Claud's efforts below.
Azel/Tailto. Despite Arvis'... you know, Azel was still convinced that he really needs to ask his bro one more time instead of condemning him for Sigurd's death. And in the same time, despite Arvis doing that, he still felt empty because Azel was not with him anymore, this really shows Arvis being more of an Anti-Villain. Of course, Manfroy had to mess everything up to ensure that Arvis thought Azel died, by ambushing Azel and turning him to stone. And then shit hit the fan for Tailtoas you know it. But it led to some things: Turns out Bloom didn't seriously ignore Tailto. After her death, the least thing he did for her is to give her a proper burial within an ice coffin within Silesse. Eventually, miracles did happen: Julia restored the petrified Azel with the power of Naga after defeating Julius, and turned out Claud used his last charge of Valkyrie Staff in order to resurrect Tailto, giving his life in process and rendering the Valkyrie Staff unusable from that point on. By the end of it, the family, including Arthur and Teeny, after having so much shits thrown at them, finally managed to get their happy reunion and ending.