Lots of good advice here. I am just posting because I wanted to confirm the basic thrust of the posts above, that the best, and really only, way to keep your iMessages working seamlessly when you are overseas with a new SIM card is in fact, as stated, to keep your USA SIM in a burner iPhone stateside while you travel. Yes you will be able to start new conversations from your USA phone number while overseas. I've done this a few times and it's a huge pain, but for people traveling for, say, a semester abroad, it's the best way to do things. The real goal is to prevent people who do not know you are overseas from being confused about why they can't reach you. Hopefully you have family stateside still who can keep an eye on your burner iPhone to keep it up and running. I imagine that even if it stopped working, your texts would continue, if not indefinitely, for some time. I haven't tested that, because I didn't want to risk something going wrong, but I don't see why the USA phone would have to remain on after the initial activation of the overseas number.