how big are the plates ?

you can get a wooden box, and glue dowels or scrim or lathe down the inside
a little wider than your plate ... kind of like a slide storage box
a microscope user would have to store microscopic slides, but taller and wider and longer

you could always build a drying rack like they did back in the day ...

i have a wooden rack ( the upper one ) and i leave them in the rack and let them dry in the open air
if i am antsy, i use a blow dryer to dry them ..