At one rehearsal, Measham took over when the conductor, Leonard Bernstein, said he wanted to hear what the orchestra sounded like from the back of the hall and called for a volunteer conductor. He then had further assistance in conducting from Bernstein. Subsequently, in his conducting career, Measham was music director of Phoenix Opera, and chief conductor of the Stetson University Summer Institute in Florida. In 1971, Measham made his Royal Festival Hall conducting debut with the LSO, when he took over from Hans Schmidt-Isserstedt at the last minute on one 2-hour rehearsal.[2]
In 1971, Measham emigrated to Western Australia and was based in Perth. He was principal conductor of the West Australian Symphony Orchestra 1974-81, and its principal guest conductor 1981-86. There he gave many first performances, and took the orchestra on its first overseas tour, to Singapore, and to the Sydney Festival, before an audience of 120,000. In 1975, he began an indoor season of three Promenade Concerts as part of the Perth International Arts Festival, modelled on The Proms. He presented a radio series for ABC Classic FM called "Both Sides Of The Podium", where orchestra players discussed their experiences working with various conductors. His other interests in Perth included yachting, and he was a member of the Claremont Yacht Club and then Mounts Bay Sailing Club where he raced his own keel-boat.
Measham died of cancer of the pancreas, in Perth. His early marriage to the soprano Susan Shoemaker ended in divorce. His two children from his marriage, Aaron and Guenevere, survive him.