Systematized suburi practice is present in some but not all koryu kenjutsu, though I don't think there are any systems that do nearly as much as Saito Sensei's or other Aikido suburi systems.
Ono-ha Itto ryu, when I saw them train a couple years ago, would practice their standard kamae, and then do a simple series of straight cuts from their In and Yo kamae, which are essentially right and left hasso.
I have seen a type of suburi practice from, I believe, Muto ryu, where the sword is raised to jodan and a deep breath is drawn in and packed down into the hara. A deep, long-reaching cut is made and the swordsman fully exhales...then, when there is absolutely no air in the lungs, the swordsman exhales a bit more.
Probably one of the most interesting I have seen is that in Jiki Shinkage ryu, where it is sufficiently integrated into their training that they demonstrate it at embu. Also, they apparently like to use the entire tree as a suburito, which is called a furibo.
Sokaku Takeda practiced Jiki Shinkage ryu and brought this type of suburi into Daito ryu. Thanks to Chris Li we can see that Sagawa enjoyed this type of suburi.
(I am not actually sure that this is called "suburi" in Jiki Shinkage ryu.)