This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Break Blade
Although the relationship between Hodr and Sigyn usually gets Die for Our Ship treatment, chapter 56 still tugs at the heartstrings. Before the manga began Hodr gave Sigyn divorce papers to try and use Loophole Abuse on the fact that the Athenians planned to execute the entire royal family (that is, just Hodr and Sigyn). The previous chapter ended with Hodr tearing up the signed divorce papers Sigyn handed back to him, since with the Athenian army gone, that point was moot. Chapter 56 starts with revealing that it was just an Imagine Spot. In reality, he calmly took the papers, implied that she should be with Lygatt, and she left. Poor bastard.
This is YMMV but it particularly pisses off the particular troper who despite wanting Rygart to be with Sigyn, really wanted Hodr to fight for her love fair & square, with his best pal, in a gentlemanly way. It sucks that he had to go do this & just give up.
Hodr gets more Woobie points again in Ch. 61, where he finally admits (discreetly) to Rygart that he actually is still in love with Sigyn—not as a declaration of war to Rygart, but while calling the man out for ignoring Sigyn's feelings. The sad smile on Hodr's face really just sums up all of his feelings on the matter.
In the flashback chapter, Lygartt quits college, and Sigyn tries to stop him. He laughs off the whole thing, saying that as an un-sorcerer he can't hope for anything more than being a farmer, while Sigyn is going to become a high-class scientist. Sigyn mutters about how as long as she had some books and could go to the library once a month, she'd be fine being married to a farmer...but Lygartt doesn't hear her.
The end of Chapter 52 had this troper in tears, literally. Rygart flees the party and reasons about how he is not a true hero, thinking that "There were stronger people than [him]" complete with a picture of Girge. He then finds himself at the military graveyard where he runs into Baldr sitting at a grave and drinking. He joins him and they talk for a moment before other soldiers join them and they start celebrating. They goof around and have fun, all this while sitting on Girge's grave. The whole scene is designed to be rather cheerful, but considering how Girge was and how he was treated by his fellow soldiers and especially his father makes this really heart wrenching. The reason and way he died has reached everyone and now he is no longer considered a monster, but a hero.
This is also one of the few times the readers see that Baldr actually did care about his son.
Everything about Girge's death, for that matter. From the scene itself to why he did it to the aftermath—the entire thing is incredibly heartbreaking.
Narvi's reaction after learning about General True's death, in both adaptations.
In the OVA, she ends up sobbing and banging her head repeatedly, inconsolable, as Nile tries to hold her back. Loggin has to punch her and knock her out to prevent her from hurting herself.
In the manga, sometime after she learned the truth off-screen, she meets with True's wife, who apparently just learned recently herself, and breaks down crying in the woman's chest, as True's wife tells her that they were blessed to have a daughter like her mourning him.