I travel for a living and bring coral back from my trips all the time. There are multiple ways to do it but some of the best I have found are...
Large or multiple items: ask the LFS if they have a box that the corals were shipped to them in, most stores keep these and will either give them to you or sell for cheap. These will be styrofoam boxes within a cardboard box. Fill it with what you want and add a heat pack if you want but for coral I don't normally add one. I typically have them bag the corals without extra air in the bag and also double bag it (closed bag inside another bag so it has two seals). Seal the box and mark it fragile, add contact info incase sticker falls off (name and phone #, never put your home address on luggage!!). Don't mark it "Live Animals" or anything like that because some airlines won't take a box that is marked as such.
TSA doesn't care one way or the other but the airline may not except it. I found this out the hard way once after spending $300 or so on frags but that was the only time in 6+ years of doing this that I lost something.
Smaller items: I bought a coffee thermos from WM in the sporting section that had a large mouth. I would then just add the bags of frags to the inside and then put it in checked bag.
TSA will check your bag but they typically just check the thermos and then put everything back. I have never lost anything due to
TSA.
The best way I have found to bring frags home: **This will work for most corals since they produce a slime coat but I probably wouldn't take the chance with that $500 frag**. I get some paper towel or napkins from the hotel or store and pour the water from the bag onto the paper towel so it's soaked. Then wrap the damp paper towel around the frag and put it back into the bag. Make sure you don't have extra water in the bag. Then you can just bring your frag with you in your carry on bag. This works really well for Zoa's / Palys / Acans and such but I have done it with sps as well without issues. I have never lost a frag doing it this way. I typically wrap them in the paper towel as close to leaving for the airport as I can to minimize the amount of time out of water.
I will see if I can find the article that I read about this method and the study that was done. That is where I originally got the idea and it's actually the only way I bring things back now unless I have a whole box full.
