I've done this with two quaker parrots (Myiopsitta monachus), first by plane from the US to Europe, and some years later, by ferry from one European country to another one.
First of all, you may be overlooking something. As far as I know you don't need export and import permits for cockatiels (CITES), but make very sure because pets, and certainly birds, can be taken away by customs if you don't have the right papers. This almost happened to me after one country's department had given me the wrong information; fortunately, I had that letter with me, but we were still kept at the airport for hours.
Second, you'll also need a health certificates. Ask your avian vet about this, and also look at the requirements of the country you are going to. There are time constraints; sometimes, the paperwork needs to be sent to, approved by and returned by an agency and any testing (test results) may take time too.
Third, now I am getting to the heart of your question.
Do these two tiels normally live in the same cage? Then get one travel carrier and get them used to the carrier. I had a Doskocil cabin carrier that was - and still is - excellent; I'll see if I can add an image later. I got my birds used to that and to the excitement of travel before the actual journey. I had been told that such travels can be very stressful for birds, so I wanted to prepare them as well as I could. It's great that you'll be traveling with two birds as they'll reassure each other.
Are your birds' wings clipped or not? If not, then go to your avian vet and have their wings clipped (also so that there is less chance of the birds injuring themselves as these are tiels). (For me, the idea that something might happen on the way and the birds would escape was very hard and that's why I did it.) If you do this well in advance, the shocks won't happen all at once for your birds. In the new country, their temporary dependence on you will be good for bonding and reassurance.
It is very rarely possible to travel internationally with pets in the plane's passenger cabin. It is possible that first-class passengers can sometimes get away with it.
When you travel, secure the carrier, by which I mean that in the unlikely event that the carrier falls, it won't open. One or two pieces of string is all it takes. Have spare pieces of string with you,too.
If you are going from, say, Florida to a country with colder weather, make sure you have something on the other end that helps keep them warm (and you may also consider getting cage heating there). We were lucky, we arrived in hot weather. Take food, treats, water with you or have someone waiting on the other side with those supplies if you can. A hot-water bottle, wrapped in a towel, or in its own cover, or put under the carrier can help. (But make sure the birds don't overheat either.)
And, talking with them about what's about to happen, in a reassuring manner that tells them something is up but everything will be fine helps a lot too. It helps tremendously helpful that birds are so intelligent because it means you can work with that, with them.
Rest assured that my two quakers did perfectly fine!
I have later had a cockatiel too, and yes, tiels have a slightly different character and pre-travel training, walking around with the birds in their carrier, taking them all sorts of places with noise and so on, may really help a lot with cockatiels.
This is a long answer to an old question, but it may help someone else one day.
Finally, here is an image of a slightly different carrier than I have and an image of one that has a small sliding wire door in the top like mine has. This one (link to reputable online parrot product store) is also very suitable.