As a result of several unfortunate experiences, we do not recommend using any courier company. However, there are a number of shipping companies these days that do professionally transport stained glass windows, so it may be worth one's time to investigate and call various agencies to see if this is possible. To professionally ship windows, the process requires special crating and the use of a wooden pallet.
Moving Windows By Car
Windows will travel safely and best when in a vertical position (the small sized ones can sometimes be carried when horizontal). Larger windows that are unable to be placed vertically in the vehicle can be placed horizontally, so long as they have adequate support underneath the glass in the centre.
Do not be lulled into a false sense of security by putting corrugated paper around a window. It may protect the glass and frame from a scratch, but it will not protect against breakage. The window must be secured by having it's wooden frame held/attached.
Taking Windows On A Plane
We have several customers who say they have done this. Our suggestion is that you speak with your airline and consider carrying it on in a clear plastic bag, and ask that it be put in the garment closet.