Icelandair! Their box requirements are about the same as Amtrak's. The box is huge. It cost us $58 a bike from Portland, OR to Amsterdam.
Get the biggest box your LBS will give you. A 60cm frame will be a challenge, but I have done it with my 58cm quite easily. Also ask for a fork protector and a rear derailleur protector that come on all bike shipped to the shop from the factory. They also have other plastic protection goodies that they will probably be glad to give you. They usually have a box of this "stuff" sitting around. Our local shop is great to work with. Remember that the box will get inspected at security, so do not use too much tape on the top.
Pad things well because the boxes will take a beating. This one was put on 4 different flights, and came through OK. Put a label with your name, address, phone number, flight numbers, and destination on the outside of the box.
Check out Adventure Cycling's website for some hints on packing a bike. I usually put the 4 empty panniers and my helmet in the box. Pipe insulation does a good job of padding and protecting the bike's finish. I did have to take my front rack and fender off to make it fit in a used bike shop box. Place the pedals in a zip lock bag and tape in one of the water bottle cages. Remove quick release skewer from the front wheel, and zip tie to seat tube. The bike is always packed better when leaving from home than on the return trip.
It is a relatively easy matter to reassemble your bike when you get to your destination.
My bike in the background is pretty much the way it came out of the box. The empty panniers were on it during shipment. I only had to remove the pedals and remove the bars and stem to make it fit. The large box is from Schiphol Airport in The Netherlands. Icelandair accepted the box with no problem. This was at PDX getting ready to ride the 120 miles home from the airport.