Supreme Court, Court
Capitalize all forms of the U.S. Supreme Court:
U.S. Supreme Court
Supreme Court, the Court
For other courts capitalize only when exact and full name is given:
Supreme Court of Pennsylvania
Pennsylvania's supreme court, the court
the U.S. District Court for the District of Arizona
the U.S. District Court for Arizona
the district court, the court
Supreme Court of Maryland, Maryland's supreme court, the court
Court of Appeals for the Ninth Circuit, the circuit court, the court
the Court of St. James's, the court