QUOTE(playpen)
I have many cigar boxes and they air out nicely but why bother? The aroma is nice!
Yes... unless you have allergies, or asthma, or emphysema, or have spent great effort in quitting smoking and don't want to be reminded, or just dislike tobacco smells.

Mary A, I asked the same question a while ago. I'm asthmatic and allergic to tobacco, my folks quit smoking after many years and with great effort, and my mother has mild emphysema. For all of these reasons, killing the cigar smell was
very important... and also for the aesthetic reason that I don't want my pens to smell like stogies.

The answer given here was that there probably wouldn't be much residual aroma, and I could eliminate any there was by airing the boxes out, or by filling them with cedar shavings (as used in pet cages) for about a week. So I went to the tobacconist's shop and picked up some very nice cigar boxes. When I got them home, the smell was overpowering. I left them out in the garage for a week and a half, and it didn't diminish
at all. So, beginning to worry a bit, I filled them with cedar shavings. Three days passed, and they smelled like tobacco and cedar. Three more, still tobacco and cedar. Finally, yesterday, after a week and a half with the cedar, I opened them... and no scent but fresh, clean cedar reached my nose!
And there was much rejoicing!
Now, this is an extreme case. The cigar shop had a sign on the door reading, "THIS IS A WORK-FREE SMOKE PLACE." The owner and another person who seemed to be a friend or employee (he spoke with a heavy accent, Russian I think, and I couldn't catch much of what he said... it was rather surreal and intriguing) were both smoking gigantic cigars. Even though there were only two people in the store, it was so filled with smoke that the haze was visible through the windows, hanging from the ceiling down to about two feet from the floor. I was sick for two days afterward, the miasma was so thick. These boxes had been steeping in pure tobacco smoke for who knows how many weeks or months, and with my allergies and asthma, I would notice and be bothered by even the weakest leftover scent.
If cedar shavings will work even on the most smoke-impregnated boxes, for the most smoke-intolerant people, then I'm sure it will work for you (and probably a bit more swiftly as well).