, you catch monsters in balls, and store them digitally. Somehow.
I hadn't planned on establishing an equivalent for Grace-A-Monsters, but then I got to the comic I had intended for today, and the comic to follow it. The lack of "storage" for Gracemander was a problem for the staging and timing of those comics, and I (eventually) realized I had to establish an explanation before those comics (hence how this wound up late in spite of George appropriate copy/paste action).
None of the trainers have been carrying around "pokeball" equivalents, but I considered various scripts that made a joke about "Grace-A-Spheres" anyway. It's apparent where I eventually wound up, however, and I like them just going to this other universe / dimension / whatever as appropriate and by their own will more than any other options anyway.