What I did was to check the Yellow Page listings for movers, and selected 3 or 4 that indicate that they do international moves. Call them and set up an appointment for them to do a quotation for you. That gives you a chance to see how they work (to some extent).
With an international move, you'll be working with the local moving company on each end and it's important to feel comfortable with the people you'll actually be working with. Be sure to ask them about insurance and customs clearance.
Cheers,
Bev