A miter saw is one of the more portable shop tools, since most compound and sliding models include a built-in transport lock made exactly for this. Engaging that lock and protecting the blade are really the only two things that matter.
Pro tip: If you still have the original cardboard box, it is genuinely the best case for a miter saw; the molded foam holds the head locked better than blankets alone.
Watch out: Never carry a miter saw with the transport lock disengaged; the spring-loaded head can drop or swing and pinch fingers or crack the fence.