But in any case - emerses or submersed growth - the roots is what matters. If the plants are not just stem plant trimmings and actually have roots make sure that they are disturbed as little as possible during removing from the substrate. It's best to ship them in the substrate, with a small amount of it. Don't just pull them out.
Wrap the plant in wet paper towel. Do not put any extra water. Put the plant wrapped in the wet paper towel in a ziplock bag. Expell all the air. Wrap the ziplock bag in newspaper. Put in a styrofoam insulated box. Add heat or cold pack that is placed AWAY from the plant and wrapped in newspaper too.
That is how plants ship best. Usually people don't do the entire packaging but most plants still make it.
I find that expelling the air works for short trips... great for taking plants in a suitcase... and for up to a few days in transit... but some plants dont fare well for much longer. You never know when the 2-day priority mail will take 5. I like to ship my plants - emersed or submersed grown in a plastic bag with air space..or in a take-out stryo like you find on the salad bar enclosed on a plastic bag (also from the supermarket).... in either case, only with a little moisture in side. As long as the plants are in 100 % enclosed humid environment, they will do fine.
For the flat food styros, I line them with 1 sheet of newspaper or old phone book (thats how i recycle mine). The moisture they soak up is sufficient. I shake out the extra water. These take out containers fit into the free Priority mail boxes. This way, you can ship a lot of plants for under the 1 pound charge of $4.80.