A royal warrant of appointment is a document which allows a company to trade with the British Royal Family. If you're looking for synonyms for this phrase, you might consider "royal appointment", "royal sanction", or "royal approval". Other phrases that could be used include "authorized by the royal family", "granted a royal concession", or "endorsed by the crown". Essentially, any phrase that indicates an official endorsement or approval by the British royal family could be considered a synonym for this term. These phrases are often used in business contexts, particularly in industries that supply goods and services to the British royal family.