Although the two never interacted in-game due to Rantaro's early death but both were part of Kaito Momota's strategy team meeting. During Rantaro's body discovery she was one of the very few students who weren't in complete shock. But in Chapter 6, during the final investigation Himiko and Shuichi discover a USB drive in Rantaro's Ultimate lab that was hidden away in a safe which included Rantaro's video message for himself before he lost his memories, afterwards watching the video message Himiko wonders why Rantaro would do something so stupid (join another killing game and survive).
They mainly interacted in Danganronpa V3's Anthology Series in Volume 2, Chapter 7, "Magical Training for Adulthood" by Itagaki Hako, as where Himiko falls down and a concerned Rantaro goes and helps her by bandaging some of the scrapes on her leg due to falling. Himiko tells Rantaro that he's really used to treating injuries like these and Rantaro answers back due to him having a lot of younger sisters, also Rantaro answers that Himiko reminds her of his little sisters. In order to repay Himiko plays hide and seek with Rantaro. Eventually Rantaro finds Himiko doing a magic trick in the gym. Worried, Rantaro is afraid for Himiko's safety as she's in a much higher place than usual and Rantaro is afraid she might fall from the place and constantly asks her if she's okay at a high place. Himiko suddenly starts falls but luckily Rantaro rescues her in time due to his adventurous skills from his travels.
The ship sailed due to Himiko being reminded as Rantaro's younger sisters in the anthology series. The ship isn't very popular due to having other major ship rivals like Amamatsu and Tenmiko, but a few feel like that Himiko and Rantaro would have a little sister and big brother type of bond instead rather than a romantic one due to Rantaro being a big brother to his twelve younger sisters as he always takes care of them also since Himiko tends to be childish in the game. This ship has a very small amount of supporters due to other popular rivals.
Some similarities they share are both losing the people they loved so suddenly before the killing game started, Rantaro was somehow losing all twelve of his sisters all around the world meanwhile Himiko's was losing her master. However, it's unknown if their respective important people truly exist due to this being a fabricated past caused by the mastermind.