This is a good place to mention, however, that since many of us live in areas prone to one disaster or another (be it hurricanes, earthquakes, tornados, blizzards, floods, etc.) everyone should have an emergency pet kit ready in case you need to evacuate the house. It should contain what you need for the animals to survive ok for a few days, keeping in mind that logistically, you can't carry with you a 4x2x2 cage plus plants and all that good stuff.
In the case of chameleons, you might want to have a big plastic tub ready with small opaque tupperware-type containers/critter keepers where you can easily transport your cham, preferably something dark so they can't see what's going on. Then something like those collapsable cylindrical cages from LLL or butterfly cages (they can live in something smaller a few days), and a few sticks, something you can put in the cage in a few minutes and give them something to hold on to. Maybe a fake vine or two from a dollar store. Then you will want to have stuff like cold packs and hot packs, because you don't know how long it will take you to get power back to find them any lights for heat. A sheet/towel would be a good idea, to cover the cage over and keep it warm or cooler with the heat/cold packs. Also include a little manual spray bottle for water or a dripper or both.
Remember that the idea is to have a bin that is lightweight and easy to carry in case of an emergency or evacuation. Your main priority is to get you and your pets out as quickly as possible and to have the basics they need to be ok a few days until you find a safe place to be or it's safe to return home. I have an emergency plastic bin with stuff for my chameleons and my dog if I needed to evacuate due to a hurricane, and I think everyone should think about having something prepared.
I wouldn't worry too much about stress. If they're under a little confusion and stress for a few days it's sad but they'll live. All you can do it try to keep it at a minimum but you can't expect to keep them in a happy bubble in an emergency. Worry about getting everyone out alive and then worry about making everything comfortable again.
