During the late 1950s Varviso made a number or notable guest conducting debuts, including the Deutsche Oper Berlin (1958), Paris Opera (1958), and the San Francisco Opera (1959), the latter being his first conducting assignment in the United States. In 1958 he conducted the world premiere of Heinrich Sutermeister's "" at the Brussels World Fair. On 10 October 1961 he returned to San Francisco to conduct the United States premiere of Britten's "A Midsummer Night's Dream". He conducted "The Marriage of Figaro" for his first performance at the Glyndebourne Festival in 1962 followed by a production of "Der Rosenkavalier" for his debut with Covent Garden later that year. He returned often to the Royal Opera throughout the rest of his career, conducting a wide repertoire which ranged from standard works by Mozart, Puccini, Strauss, and Wagner, to less frequently performed operas like Debussy's "Pelléas et Mélisande".