After the War

After the battle, Mihawk shows up in the castle on Kuraigana Island. After reading about Moriah's presumed demise, Perona starts to cry. Mihawk, without any sympathy, tells Perona to go cry elsewhere. Perona then scolds Mihawk for his inhospitality. Mihawk responds by saying that Perona intruded into his house while he was gone. He also says that despite the newspaper's assertions about Moriah having died during the battle, he was alive during the whole big confrontation between the Whitebeard Pirates and the Marines. However, Mihawk cannot give Perona a definitive answer on whether or not Moriah is indeed alive and questions the validity of the newspaper. Mihawk is unaware of the fact that Doflamingo was ordered to kill Moriah.
He's later seen in the ruins near the castle, watching Zoro's fight against the armed baboons roaming the island. He comments on how Zoro is still far away from the sea even though he was away from the castle for a long time. When Mihawk sees that the boat he provided to Zoro gets damaged, he comments that the boat is now useless, but Zoro brushes off that comment saying that he can just use part of the boat to help him swim to his destination. Mihawk then explains to Zoro the reasons behind the baboons' fighting style, and then asks him to return to the castle and leave the following morning, but Zoro refuses, saying that he needs to reach Luffy. Mihawk gives up, and allows him to do as he pleases.
Zoro later comes back and asks Mihawk to train him. Mihawk tells Zoro to go, believing such an idea to be foolish and assuming Zoro is simply incapable of defeating the baboons. However, Zoro has already defeated the baboons, and wants Mihawk to train him so that he may one day defeat Mihawk himself. In a rare moment of emotion, Mihawk laughs uncontrollably at the absurdity of him training the man who would one day duel him for the title of the strongest swordsman, but notices Zoro is putting his pride aside all for the sake of his captain. Mihawk gives in and tells Perona to heal Zoro so they can begin his training, which takes place