I throw mine on a shelf. I don't travel with my tools, so I don't need a belt or toolbox. If they get dull and/or blunt, I'll just buy new ones. They're cheap chinese tools for less than 10-20 bucks a piece, delivered to my home for free.
I've tried sharpening blades and tools and I seem to screw it up every time. Getting them sharpened would cost me more than they are worth. The only tool I own that has any sentimental value is a victorinox pocket knife I got from my mom when I was 9 years old. That one deserves professional care. All the rest is just a tool, and they are used as such.
My concave and knob cutters tend to stay sharp for at least 4-8 years at the rate of which I use them. I base this on other gardening shears I have that are of the same quality, because I haven't been into bonsai for more than 3 years.
Wire cutters are a different story, I get those at the dollar store for about 3 dollars a piece and I buy a new one every year.