When traveling internationally with a service dog, you should always keep handy the same documents you would when traveling throughout the United States. The Transportation Security Administration (TSA) recommends that people who use an animal for assistance carry appropriate identification. Identification may include cards or documentation, presence of a harness or markings on the harness, or other credible assurance of the passenger using the animal for their disability.
However, keep in mind that your documentation could be useless in other countries. The best thing to do is contact the consular’s office for the country you plan to visit at least four weeks in advance to find out what is required. Rules in foreign countries may prohibit pets from entering museums and the like. Depending on the country, your service animal may be admitted to such places.
As I’m sure you know, U.S. airlines and hotels do not charge customers with disabilities for service animals since these animals are not considered pets. However, rules vary in other countries and while guide dogs may be allowed to fly for free, even an authentic letter from a U.S. doctor confirming that an animal is a service animal in the United States may not get the fee waived on international airline carriers.