My minicaves are plastic boxes by Rubbermaid, Sterilite, and others that I bought at Walmart and Bed, Bath, and Beyond. I coined the term "minicave" because they function just like a miniature version of a cave, allowing tighter control over humidity around the cheese. That word is also shorter and easier to say than "ripening box".
Some folks have had to resort to a humidifier to add extra moisture to their cheese environment. Search on the forum for discussions about that.