I had my solitaire re-mounted into my wedding set.
I'm sure any jeweler could do this for you, but I would go with a higher end or independent company as opposed to a mall jewler. Your best bet will probably be to call and get estimates.
Be sure to check out warranties/guarantees/insurance and find out who (if anyone) will be responsible for the work.
For example, when my ring was re-set we went with a different company than the one where my FI bought my ring. So, the second company (Shane, and they are fantastic) is responsible for my current setting. They do the cleanings, inspections, re-sizing, and will replace any stones/shanks/etc. Basically they will do anything to the ring EXECPT the center stone because we didn't purchase it from them. However, if my center stone were to be lost or damaged because of the settting, they will replace it with one of a similar quality.
If anything were to happen to my center diamond, we're SOL. The store where it was purchased, voided our warranty because they didn't remove or replace the stone.