In open court is a legal term in the United States defined by the appearance by a party or their attorney in a public court session such as during a trial. Normally, the public may be present at trials, hearings and similar routine matters.
-- U.S. Const., Art. III, § 3 (emphasis added).
In the United States, the constitution guarantees criminal defendants the right to a "speedy and public trial" under the Sixth and the Fourteenth Amendments. The Sixth Amendment also grants the defendant the right to appear on his or her own behalf requiring leave of the Court in complex criminal cases, and standby counsel may still be required by the judge.
Many courts dealing with children or minors, such as the New York Surrogate's Court, Probate Court, Family court, juvenile court, or widow's and orphan's court do not normally hold sessions in open court.