Did that in November 2004 with a Jeep Wrangler.
I went with this company:
Schumacher Cargo Shipping - International Shipping for Cars, Household Goods, and Freight
I had the option of "roll on/roll off" or containerized. Went for the option of the container as that allowed me to put in some other cargo as well. It was a 20ft container and cost me 1.700 USD. That included loading, customs and insurance in NYC and offloading in AUH, for clearance in AUH I had to go with a local company (cant remember their name, somewhere in the touristclub area), cost me 400 AED. Additional cost for import plate (about 200 AED), valid for 3 or 4 days to drive up to registration (could have taken a pickup truck at similar cost as well), 5% custom duty based on the value of the car ( and they do calculate very fair on that.)
Schumacher cargo took care of everything from drop off in NYC on, even gave me the contact to that company in AUH for the offloading. The vessels sailed that time once a month and the trip takes about 4 weeks..