This got my mind working, and I was inspired and had to try it! I actually made this tutorial on my first run, so this is kind of slapdash and has some flaws, but if you take the basic concepts I think you could do some great stuff with it.
First step, measure the bottom of your cigar box. (If you're having trouble getting a measuring device down in there, a good way to do it is put a slip of paper inside with one end against one wall and smooth it along an adjacent wall, then run your fingernail in the groove between the opposite wall and floor to crease the paper at just the right length.)

My box was pretty small, 5 3/4" wide by 5 11/16" deep. That 1/16" was enough that one of my pens would only fit sideways...
But anyway, once you've got your measurements, cut one piece of cardstock to those dimensions: this is your bottom layer. Then cut another piece for your top layer out of cardstock, or just paper might work well here. Its width should equal to the dimension you want your pens to lay parallel to. Since my pens were going sideways, I used the width of 5 3/4". The length of this second piece: as long as your piece of paper, and you'll probably still need another one (more later).

Now comes the fuzzy math. On the bottom layer, on the edge perpendicular to the pens (in my case the 5 11/16" edge), you'll need to mark a little extra, then 1/4", 1/2", 1/4" . . . You need alternating quarter-inches and half-inches, starting and ending with quarter-inches, and with a smidgen left over at each end. I only had a generous 1/16", but it was enough.

Make matching markings on the opposite edge and connect them into lines with a ruler.

Now on the top layer, also on the edge perpendicular to the pens (the long-as-you-can-get-it edge), you'll also need to start with some extra space, but this will be trimmed later, so I went generous and made it an inch. Then make a mark every 1/2". Again, make matching marks on the opposite edge.

These marks define your fold lines, so instead of connecting them with a ruler and pencil, you can use a ruler and a scoring tool. Remember to protect your work surface and watch your fingers! And be gentle. I burst some seams on mine because I overdid the scoring. (If you're using lighter stock, you might be ahead to either draw pencil lines, or skip this step altogether and just fold from mark to mark.)

Now, starting from the waste edge and with the marked side (which will be the wrong side) facing you, fold the fold lines into a mountain fold, then a valley fold, then another mountain fold. Repeat this pattern: mountain valley mountain, mountain valley mountain. (Mountain and Valley are origami lingo, but pretty intuitive: a mountain fold juts toward you and a valley fold dips away.) What you should get is a series of peaks with flat beds in between, like this:

Guess where the pens go. ^_~
Fold your way across the top layer like that. Then, before you continue, count how many half-inch sections are drawn on the bottom layer, then count how many "beds" are folded in the top layer. Unless you had a really long sheet for the top or an even dinkier box than mine, you're probably short on beds.

To fix this, cut just after the last bed, as indicated, then make yourself another top layer piece. Take the number of beds you're short by, add one, multiply by three, then add one again. I was only short one bed, so...
1
+1 = 2
x 3 = 6
+1 = 7
This is the number of marks you'll have to make on the second top piece---don't forget the inch of extra before the first mark. Make the matching marks opposite and mark lines or score; you can cut the line across the last pair of marks. Fold in the same way as the first top piece, marks toward you starting from the extra M V M, M V M. You should end up with an orphaned bed at the end---just like on the first piece. Overlap those two with a light coating of glue and stick them together.

(BTW, I'm not trying to be complicated with the math, rather avoid wasted effort, so if it's easier, just mark and fold the whole dang thing, overlap it and stick it together however you want.)
Now comes the hard part, assembly. Basically, the beds on the top are going to match the half-inch sections of the bottom, and the peaks will stand up from the quarter-inch sections. And it needs that little bit at the ends to seal it up there. This is where the waste at the edge of the top part is handy---a piece of tape overhangs the small extra part of the bottom and has plenty of room to hold them together while a light coat of glue dries.

Continue down the length of both pieces, gluing the beds to the half-inch sections---ie, stick together the red-hatched areas in the pic below. Just a tack at each end is enough (I smeared the drops seen below into thin coats at each end---one of them tried to get away while I was taking the picture...)

Here it is partially done:

Actually I recommend against paperclips because it crimps the stock, worse yet while it's wet with glue and more prone to being reshaped and sticking that way. Clothespins would be better.
With it all glued and clipped, I put pens in and a book on top to try to keep it from arching as it dried:

Once dry, remove the clips, flip it over and trim off the waste from the top layer, using the edge of the bottom layer as the guide.

Then just set it in the box: you're done!

Here's mine filled with pens (ones waiting to be sent off for restoration, or for my own tinkerings with the cheaper ones). You can see I've got plenty of room in the top to make another tray and stack them.

Like I said, this one was my first effort and had some flaws. When I do it again, I probably will use lighter stock for the top layer; I was fighting the thick card this time and I don't think the extra strength is necessary there. A solid bottom layer would be good though, so the tray could be picked up and not spill, so for that I might even go heavier, like cardboard. I also realised that instead of that little 1/16" tab on the ends, I could leave no extra at the ends of the bottom layer, say 1/4" at the ends of the top layer, and turn the ends of the top layer *under* to seal the ends. Also, I used Aleene's Quick-Drying Tacky Glue because it was handy, but it wasn't the best choice as it tended to soak, soften, and warp the paper. This might be a better job for a glue stick...
But I think the concept is sound, it's pretty quick and easy, and hopefully it can be of use to some of you---I hope you can take my flawed example and run with it. With all the paper and card out there for scrapbooking and other arts and crafts, we could make some really beautiful pen trays! ^_~