Cartwright's term as Governor-General of New Zealand was from 4 April 2001 to 4 August 2006. She was succeeded by Anand Satyanand at midday on 23 August 2006. During the intervening period, Chief JusticeDame Sian Elias was the Administrator of the Government. On 16 June 2002, Cartwright made a speech at the Annual General Meeting of Save The Children's New Zealand branch, in which she criticised section 59 of the Crimes Act 1961, which allowed parents to use "reasonable force" to discipline their children. A number of groups criticised this position, such as the Society for the Promotion of Community Standards – the Monarchist League stated that these comments were "overstepping the mark" for a representative of the Queen, while Green Party MP Sue Bradford welcomed the comments. On 12 August 2002, in a speech at the opening of the Specialised Applied Research Centre of the Victoria University of Wellington, Cartwright questioned whether longer sentences would reduce criminal reoffending rates. This was after the Sentencing Act 2002 and the Parole Act 2002 were passed – Acts for which Cartwright granted Royal Assent on 12 July 2002. The Acts introduced mandatory sentences for criminal convictions, and reduced the likelihood of parole. ACT New Zealand MP Stephen Franks was critical of the remarks, stating "I don't think she was regarded as one of the most weighty judges and she's putting herself into a difficult constitutional position by weighing in this area", as was the Sensible Sentencing Trust. However, Prime Minister Helen Clark defended the governor-general, stating "One of the challenges for us is we clearly are no longer a dominion of Britain where the Governor-General is exactly like the Queen". On Waitangi Day 2004, following National leader Don Brash's controversial Orewa Speech on race relations, Cartwright controversially gave a different interpretation of the phrase "He iwi tahi tatou". Following the 2005 general election, former National deputy leader Gerry Brownlee stated that Cartwright had not allowed National the chance at forming a government. Brownlee said "I have to publicly say that I have lost respect for the Governor-General and I think it is time we sat down now and started to look at a much more formal constitution for New Zealand". In response, Helen Clark said that the governor-general followed a "very, very proper process".
Cartwright was appointed to sit as one of two international judges in the Trial Chamber of the Cambodia Tribunal by Cambodia's Supreme Council of Magistracy. Multiple Defence requests that she stand down from this position have been consistently rejected by both the Trial Chamber and Supreme Court Chambers on their merits. The Khmer Rouge was responsible for the deaths of 1.2 to 2 million people between 1975 and 1979; one in four Cambodians were killed and whole families were wiped out.