In 1962 he appeared for the government in the High Court, opposing any further delay to the execution of Robert Tait, who had been convicted of murder. He told the court that Tait would be executed the following day, but the government would comply with an order of the court, if it was made. The High Court then made an order delaying the execution. Winneke was appointed as Chief Justice of Victoria in 1964. According to Sir John Young, he was "a model of fairness", who delivered judgments which "were models of clarity and learning". He was appointed Lieutenant-Governor of Victoria in 1972. In 1974, he retired from office as Chief Justice and became the Governor of Victoria, an office which he occupied with "great distinction" until 1982. He was knighted in 1957, created a Knight Commander of the Order of St Michael and St George in 1966, a Knight Commander of the Royal Victorian Order in 1977 and a Companion of the Order of Australia in 1982. He received the honorary degree of Doctor of Laws from the University of Melbourne in 1978 and Monash University in 1980. Don Chipp said that Winneke had told him in 1971 that the convicted murderer Leith Ratten was innocent. In 1981, when Ratten had yet to be released, Chipp said Winneke denied the conversation had taken place. Later a member of the Supreme Court at the time of Ratten's trial told Tom Molomby that Winneke had wanted to remove the jury from the trial. Such a move would require a belief that the evidence would not support a guilty verdict. Winneke was married twice, first to Nancy Wilkinson in 1933 by whom he had two sons, John and Michael. Following his first wife's death in 1983, in 1984 he married Ellis Faul, who survived him. His son, John Winneke, was also a judge on the Supreme Court of Victoria, being President of the Court of Appeal from its inception in 1995 until his retirement in 2005. Winneke was a keen golfer and follower of Australian Rules Football, being at one time the number one ticket holder of Hawthorn Football Club.