"And producing his Credentials under the Signet Royal"
Signet Ring
Creative Commons Attribution Share Alike Signet - Credit: Kozuch

In Gulliver's day, literacy was rare, so few people could sign their name on important documents. Instead they would make a unique impression in wax with a personal ring or stamp. 

The impression was a seal or a signet. The king's seal was called the Signet Royal.