I was on a trip to Taiwan last week and decided to bring along a 'ukulele. Since it had to be a small uke, I decided to take the Kanile'a custom SS. I decided to take this one because the only other choice I have is the Martin style 1 and I like playing the Kanile'a a lot more, not to mention that it's also the more durable uke.
The case I used was the soprano Guardian case I got with one of my previous soprano purchases. It's actually quite a bit bigger than the soprano size, so I stuffed a t-shirt in the body compartment to keep the uke for sliding around inside. Taiwan is very humid but I packed a Herco humidifier for the plane ride. When I got the Guardian case, it didn't come with any straps so I took a strap from a Lanikai case so I can carry the case on my back. The uke plus the case is very light so it was very easy to travel with. I just threw the strap across my shoulders and it feels almost weightless on my back.
I took two flights to Taiwan this time and it was with Northwest and EVA Air. Neither airlines gave me any trouble with carrying on the uke in addition to a wheeled carry-on case I took with me. The uke made it to and from Taiwan with no problems. While I was in Taiwan, I got quite a bit of playing time in while we watched my kids at my in-laws home (it was not an exciting trip). I practiced Jake Shimabukuro's "Touch" for a possible performance at a friend's wedding in June and I think I have it learned now.
This is the first time I took a 'ukulele this far and it worked out great. Ukes are perfect travel companions and I'm definitely taking mine on many future trips away from home.