Air travel:
Hard case with a padlock for handgun;
Ammunition in factory box;
Both of above in your suitcase;
Check TSA website;
Check Airline website (oddly, these vary);
Declare at check in, and obey.
FYI
Our wonderful local airport has a smaller limit on ammunition than TSA. Same weight limit, but have as many rounds.
While your at it, check your carry on bags for spare ammunition! The strip search isn't too bad, but the cavity prob search sucks

I carried in Charlotte last fall, and it went well. They have some things we aren't used to but easy to deal with.