Mr. Riordan was selected by the Second Judicial District Judiciary to serve as the Children's Court Judge. As the Children's Court Judge Mr. Riordan presided over jury and non-jury trials for allegations of delinquent conduct by persons under the age of 18 from 1978 to 1980. Mr. Riordan also reviewed procedures of, established policy for, and exercised general supervisory control over the Juvenile Probation Department and presided over trials involving allegations of child neglect and abuse.

In 1980, Mr. Riordan was elected to the New Mexico Supreme Court. As one of five Justices of the New Mexico Supreme Court, Mr. Riordan spent much of his time writing opinions to be published, authoring decisions which were not to be published and supervising two law clerks and a secretary who assisted with these activities.

In 1986, Mr. Riordan was elected by the remaining Justices of the court to serve as Chief Justice of the New Mexico Supreme Court. As Chief Justice Mr. Riordan managed the day-to-day administration of the Supreme Court in addition to handling a full appellate caseload. Mr. Riordan also served as spokesman for the Court, representing the judicial branch of government to the public, appearing before legislative committees, in communication with the State Bar of New Mexico, President of the New Mexico Compilation Commission which is responsible for the publication of New Mexico's statutes and court decisions.

Since 1992, Mr. Riordan has developed a dynamic mediation and arbitration practice handling over 2000 cases, many of which have been referred by various District Court Judges.