Capitalize “U.S. Supreme Court” and also “the Supreme Court” when the context makes the U.S. designation unnecessary.
The chief justice is properly the “chief justice of the United States,” not “chief justice of the Supreme Court.”
- Chief Justice John Roberts
The proper title for the eight other members of the court is “associate justice.” When used as a formal title before a name, it should be shortened to “justice” unless there are special circumstances.
- Justice Antonin Scalia
- Associate Justice Antonin Scalia
See also AP Style Judge.