My name is Angela, I am a New Zealander, married to an American, and we have three children, ages 3, 5 and 7. We travel to New Zealand a lot which for anyone who knows anything about what that entails, you can appreciate how long and complicated that can be - 3 kids, 12 hour flight from LA to Auckland, not to mention any connecting flights. International security, customs etc, it's a whole different ball game.
Last year I decided to take our kids home to New Zealand - on my own - the week after school got out, for a three week vacation. We had to fly from Colorado to California and then on to Auckland - and back again. It was hot summer here in the US, but cold rainy winter in New Zealand, so it meant a lot of packing and a lot of luggage. I have travelled through LAX so many times to know you don't mess around without being in control of yourself, your family, your luggage and your destination. I knew I could control everything but keeping track of kids while checking in at counters, or at baggage claim, or on curbsides - we all know how they can wander. So I needed something to help me....then I had an idea.

I went to Home Ddepot and bought three carabina bungy cords for less than $5each. They are thick, hard elasticated bungy cords which measure about 4-5 feet in length and have carabinas on both ends. I clipped the one end to the child - on a belt loop (when planning their clothes for the day I had especially chosen clothes with belt loops), and the other end either to myself if we didn't have a cart - like after you have gone through airport security, or to the cart if I was pushing luggage. It meant the kids were able to walk freely but not far away from me, and no one got lost. Of course we had a few funny moments when lamp posts came our way, but we quickly figured it out.

On our maiden walk with the cords attached I was stopped 7 times by parents asking me where I got them, and complimenting me on what a great idea. That was just the beginning. Airline crew told me it was one of the best ideas they had seen, as all too often kids get away from the parents and the parent has to make chase leaving an unattended handbag or luggage or other child. I didn't use them like a leash - so when we were seated waiting at places I just clipped them off - and I made it very clear to the kids that only I clipped them on and off, that it wasn't a toy and why it was important - using the movie Home Alone 1 helped drum that message home, how busy airports can be and how quickly and unintentially you can get separated.

I was allowed to take them onboard in my carry on luggage and they bundle up so small it wasn't an issue at all.  On a different trip I did, domestically, I actually put them in the front zipper of my checked bag and after claiming it at baggage claim I whipped them out.  Either way worked perfectly find.  They don't breach security at all.

I hope you have as much luck as we did. I have travel planned this summer and plan on using them again, and also for another trip to New Zealand later in the year. For less than $15 I knew I wasn't going to lose my kids or find myself in a compromising position, true peace of mind.

The photo attached is taken at Auckland airport in the parking/loading area outside and a little dark to see, but you can sort of make out the cords that I have in my hand after attaching them to each of the kids and to the cart.
I have also attached a photo from the Home Depot website of the item.

This is the link to the Home Depot site showing what I purchased.
http://www.homedepot.com/h_d1/N-5yc1v/R-100185918/h_d2/ProductDisplay?langId=-1&storeId=10051&catalogId=10053

This is the product description incase the link fails
The Keeper 48 in. Carabiner-Style Bungee Cord features an aluminum carabiner hook that locks and secures onto any anchor system. The carabiner hook is stronger than a conventional hook. The super-duty bungee is exceptionally strong.

Ideal for heavy-duty securing
Super-duty bungee is stronger than conventional cords
Carabiner-style, aluminum hook locks and secures onto any anchor point
Spring-gate design makes it easy to quickly secure the bungee
MFG Brand Name : Keeper
MFG Model # : 06158
MFG Part # : 06158