Take them on the airplane, hook them in, and strap your children into them just like in the car. This is what is safest, and should be what you do. Putting your carseat in checked baggage can be the same as a car accident, they don't care if its a carseat or anything else, it will be tossed under the plane with heavy bags thrown on top of it, jostled around during flight with more heavy bags on top of it, then taken off the plane and thrown into the baggage cart, rolled down large 'hills' to get to baggage claim at your destination. IT WILL GET DAMAGED. Just because you cant' see the damage doesn't mean its not there, plastic is just plastic and its a carseat, its a pretty important piece of plastic since you will be depending on it to save your childs life in an accident, and with unseen damage to seat by airline checking into baggage... it compromises its safety.
Take your seats on the plane, and use them just like you would in the car. Trust me your kids will be much more comfortable, and so will you.
Obviously if you didn't buy a seat for a child under age 2.... then you can't do this. but then BRING THE SEAT TO THE GATE WITH YOU and request it be put in the closet by the door you enter the plane. At least hten its not treated like it would be in baggage and susceptable to being damaged and no longer safe in a crash.
IN RESPONSE TO THE 'if its meant to withstand a crash, it'll be ok under luggage' COMMENT- yes, a carseat was meant to withstand a crash... ONE TIME. After a crash you destroy a carseat nad never use it again, regardless of the crash dynamic, its never safe to use one again. I consider a 75lb suitecase thrown on top of a carseat the same as a crash, especially when in flight its jostled around and damaged, and then put down the chute to baggage claim. So yes, it is meant to withstand a crash, but then you can't use it again after a crash.