Roukanken and Hakurouken
Roukanken is a long-bladed katana said to be made by youkai, too long to be wielded by normal humans. It's said that it has the power to kill ten spirits in one stroke, but as one cannot actually kill spirits, the truth of this claim is debatable. Youmu herself claims that "The things that cannot be cut by my Roukanken, forged by youkai, are close to none!" Roukanken's sheath has a flower on top of it attached with a seal and a little rope.
Hakurouken is the ancestral wakizashi of the Konpaku family, which only they are capable of using. It has the power to dispel the confusion of those it cuts. That is, using it on humans will cause them minor pain and discomfort, while using it on ghosts will send them to nirvana. In Youmu's ending in Phantasmagoria of Flower View, Eiki Shiki, Yamaxanadu is indirectly mentioned to have explained that what Youmu is doing to the spirits is something that is not allowed, as it can send them straight to Heaven regardless of if they deserve to go there or not.
Youmu with Roukanken and Hakurouken in Perfect Memento in Strict Sense