OneEntry.com is a free service designed to help you find and compare moving companies. National companies as well as internatioanl moving companies.
Once you have found and decided on the moving company for your international moving, create a moving inventory of all your belongings before they are packed and get a binding estimate from the removalists.
Contact on of the moving companies and make sure the correct amount is written in the moving contract. Be sure all charges are listed and don't forget to ask about expected extras and have them also written into the moving contract.
Ask about the moving company on-time record making sure they guarantee the hours the job will take, allowing an overrun of no more than 10%. By law Movers are limited regarding what they pay for lost or damaged goods - to cover potential damage, check existing insurance policy or take out moving insurance.