Norman also performed Arnold Schoenberg's Gurre-Lieder and his one-woman opera Erwartung. In 1989, she appeared at the Metropolitan Opera for a performance of Erwartung that marked the company's first single-character production. It was presented in a double bill with Bartók's Bluebeard's Castle, with Norman playing Judith. Both operas were broadcast nationally. That same year, she was the featured soloist with Zubin Mehta and the New York Philharmonic in the opening concert of its 148th season, which PBS telecast live. She performed at the Hong Kong Cultural Centre opening and gave a recital at the National Theater and Concert Hall in Taipei.
Also in 1989, Norman was invited to sing the French national anthem, La Marseillaise, to celebrate the 200th anniversary of the French Revolution on July 14. Her rendition was delivered at the Place de la Concorde in Paris, in a costume designed by Azzedine Alaïa as part of an elaborate pageant orchestrated by avant-garde designer Jean-Paul Goude. This event was the inspiration that led the South African poet Lawrence Mduduzi Ndlovu to write a poem titled "I Shall Be Heard" dedicated to Norman. The poem appears in Ndlovu's book of poems In Quiet Realm, the foreword to which is penned by Norman.