In 1952, he issued an arrest warrant for Judy Garland to compel her to testify in the divorce trial of her boyfriend, Sid Luft, from his wife, the actress Lynn Bari.

[9][10][11] In 1958, he was appointed presiding judge of the Los Angeles County Superior Court,[12] and published a book on divorce, With This Ring.

[20][21] Burke helped to create the National College for State Judges and its California counterpart; he served as chairman of the Section on Judicial Administration of the American Bar Association[22] and of the Appellate Judges' Conference; and was an officer of the American Judicature Society.

In 1970, Burke was considered for appointment to the U.S. Supreme Court and as a candidate for California chief justice.

[2][21] The family lived in Montebello next to Burke's brother and law partner, Martin, and their mother, Lucie.