Seaway Export offers car export services from USA to Croatia via following ports of loading (POLs):

Port of Savannah

Ocean container with final destination of Croatia will be delivered to one of the following ocean ports: Ploce and Rijeka.
 
We also offer Roll-on Roll-off service to the port of Rijeka for oversized equipment, such as tractors, combines, excavators, graders, buldozers, asphalt and concrete machines, other agricultural and construction machinery.

Croatia ports are serviced by all major shipping lines, including APL, Maersk, MSC, Evergreen, OOCL and others. Service offerings will be weekly and even more often. The transit time from US East coast will be 24-27 days, and from West coast around 34-38 days.

Most vehicles, motorcycles and heavy machinery can be easily imported into Croatia without major goverment restrictions.