I had no idea how to ship a Moped. I made a google search and eventually came-up with uShip which said they ship motorcycles, scooters, etc.
I found it very easy to post what I needed and very soon I received a number of bids which said they would pick-up and deliver the Moped. I selected the shipper who had the most positive feedbacks even though it was not the lowest bid.
I would use uShip again.