Generally snakes fare best when transported in a bag, either a pillowcase or snake bag work well. Lizards do best in a solid sided enclosure, preferably one that they can't see through to help minimize stress. In both cases adding some shredded paper for them to brace against/act as insulation can also be helpful.

Bring papertowels, too. Something about a car ride almost always guarantees a bowel movement, especially with lizards!

-Jen