When I broke up with my ex, we both said that it would be a shame to loose the friendship as well, she said this was a reason she did not want to break up.
We broke up 2 years ago, but we still see eachother regularly (at least once a month) for coffee or we go sailing or canoeing for the day.
For us, it is not awkward, it is good to have a friend you see regularly, and who knows you so well, that you can explain any issues you have in your daily live with, knoiwing that they understand why some things are a problem for you. I am glad I have this friendship and I wouldn't miss it for the world.