Map to Globe is an online tool that allows you to transfer a flat map onto a globe. Adam Whitehead has been trying it out with fantasy maps. Some work better than others. Westeros is not one of them, “because the maps of the North and the lands beyond the Wall need to be adjusted so they work on a globe.” Think of it as sort of a Mercator problem in reverse: imagining a flat map rather than a round world: the flat map’s lack of distortion is the issue.
As discussed before, in creating the maps of Westeros and Essos for A Song of Ice and Fire, George R. R. Martin has not really taken projection into account at all. On his maps of Westeros, the Wall is 300 miles long but the distance between Deepwood Motte and Winterfell (hundreds of miles to the south) is also said to be 300 miles long and the south coast of Westeros—3,000 miles south of the Wall!—is said to be 1,200 miles long. These are all in perfect scale to one another, which is not really possible when you look at the maps as a representation of what the planet actually looks like.
Trying to circle the square, so to speak, leads to complications, as Whitehead points out on his Atlas of Ice and Fire blog.
Of course, if your fantasy world is flat instead of round, you don’t have this problem.