If you want a mover to handle your boxes, check the phone book for moving companies that specifically state that they do international moving. This is at least some indication that they can and will handle the customs clearance for you.

If you have any contacts at a large international company in the area, see if you can find out who they use for company relocations. Otherwise, you're kind of stuck having to evaluate them yourself. Get at least two or three estimates before you decide - and ask about insurance and customs clearance specifically to make sure the companies you are talking to can meet your needs.
Cheers,
Bev