As much as I like using GUIDs as the unique identifiers in my system, it is not very user-friendly for fields like an order number where a customer may have to repeat that to a
One solution would be to take the hash of some field of the order. This will not guarantee that it is unique from the order numbers of all of the other orders, but the likelihood of a collision is very low. I would imagine that without "doing a round trip to the database" it would be challenging to make sure that the order number is unique.
In case you are not familiar with hash functions, the wikipedia page is pretty good.