This is trickier than people give it credit for because 1) You shouldn't ever type your seed into the computer in case of malware, & 2) the Human brain basically can't be trusted to remember something that long.
At home you should use a metal seed vault that you hide and then memorize a password to the wallet it backs up. Basically, to travel with your seed your job is to leave that at home but make that seed phrase virtual & encrypted with your password so it can be transported or parked online without anyone else being able to read it.
Here's how to do that safely:
  1. Download Tails (https://tails.net) and flash it to a jump drive.
  2. Grab a disconnected laptop and boot it into tails.
  3. Once that boots, create a word document in open office.
  4. Type in your seed phrase. (Make sure no one is in your room and no cameras are pointed your way)
  5. Save the file with encryption. Use a really great password for this, 13+ characters with numbers and special characters, etc. It's your money this password protects! -But of course it has to be a password you can remember. (So maybe it's ok to use the same PW here as your existing wallet PW again. You don't want to risk memorizing both.) You are your worst threat here.
  6. Rename the file something innocuous like 'party_invitation.doc' or whatever doesn't sound interesting to custom officials.
  7. Send it to your phone over a USB cable, or to a cloud account you know you can access from other countries.
  8. Test it.
That's it, just be damn sure you've memorized your longass password backwards and forwards. And if you know you're going to be using it on the other side, bring that Tails drive to open it under on that side... Because other computers may have malware at that stage.
Good luck!