Privateers played a major role in American naval activities during the American Revolution. With permission from the government, privately owned ships could attempt to capture an enemy ship. If the capture was judged to be legal, the contents and ship would be sold – and the profits redistributed to the crew.
At the start of the Revolution, most of the captures were judged on the colony or state level. The Continental Congress gave the right of appeals to the federal system on 25 November 1775 but never set up a formal court. On January 1780, the Continental Congress established a court of “trial of all appeals from the courts of admiralty” to serve as the final appeal. Later called the Court of Appeal in Cases of Capture, it remained active until 1786 or 1787.
The records of this court have been digitized and are available on Fold3. The Wikipedia article on this topic is excellent.