I'm Talking disbanded in 1987, and Ceberano released her debut solo jazz album in that same year. Kate Ceberano and Her Septet, featuring her brother Phil and veteran session musicians Alex Pertout and Jex Saarelaht, became a huge hit, and was followed in 1988 by You've Always Got the Blues, which featured Ceberano and Wendy Matthews a vocalists. In 1988 the first single from Ceberano's eagerly awaited first pop album was released. "Bedroom Eyes" became the highest-selling Australian single of 1988 and helped Ceberano win two ARIA awards for best female vocalist in 1988 and 1989. The album, Brave, was released in 1989 and went triple platinum.
"Young Boys Are My Weakness" was also released as a single from this disc. Another jazz album called Like Now followed in 1990, then her second pop album, Think About It, appeared in 1991. However, it could not build on the success of Brave and failed to produce a strong single. 1992 saw a stage production of Jesus Christ Superstar open in Australia. Ceberano won the part of Mary Magdalene, and performed alongside John Farnham, Noiseworks frontman Jon Stevens, and former Rose Tattoo lead singer Angry Anderson in the show. The Australian cast album went four-times platinum and Ceberano's song from the production — "I Don't Know How to Love Him" — was released as a single. In 1996, another pop album, Blue Box, was released, and this was followed in 1998 with Pash. The '60s-influenced pop of the title track became her biggest hit since "Bedroom Eyes." A best-of collection entitled True Romantic appeared in 1999.