The short answer is that it doesn't, of course (unless you're into collecting golf-style pencils). But when roaming the halls of an IKEA store, I came across a plastic DVD rack, and the light bulb went on.
The plastic can be cut to fit, so it was easy to install it in the drawers I got from Lee Valley.
The rack holds all but the largest pens, and keeps them from banging against each other when I open the drawers. What a great find!