Take a Ziploc bag spacious enough to fit the entire cigar box inside and poke small holes in both sides of the bag to ventilate it. Insert the open cigar box inside the bag and seal it.  A quart-sized bag will probably be sufficient for most smaller cigar boxes; anything bigger will likely require a gallon-sized bag. Don’t make the holes too large, or the cigars may become oversaturated as they sit. A paperclip or the point of a knife should work fine for poking small holes. Wet a sponge and ring out the excess water. Place the sponge at the bottom of a second, larger Ziploc bag. This will provide an artificial source of moisture from which the cigars can be revived.  Make sure to use a new sponge, and, if possible, wet it with bottled or distilled water. Old, used sponges and tap water are filled with bacteria and chemicals that can cause your cigars to mold.  Re-wet the sponge every couple of days when you rotate the cigars. Slide the ventilated bag containing the open cigar box into the second bag containing the sponge. Seal the second bag to lock in the moisture of the sponge, which will slowly diffuse through the ventilated bag and into the dry cigars. Rehydration with this method will probably take a week or longer. Don’t let the cigars become wet. A wet cigar is a separate problem. Take a look at the bags every couple of days to re-wet the sponge and test to see if the cigars are absorbing moisture. Rotate each cigar a quarter turn for even moisture distribution; switch up their positions inside the box if necessary.
Poke holes in a large Ziploc bag and place the cigar box inside. Take a second bag and place a damp sponge inside. Seal the bag with the cigars inside the second bag. Find an out of the way place to leave the two bags to take effect.