If your ancestor came from Australia
There are very few passenger lists available for trans-Tasman voyages, apart from those published in the shipping columns of newspapers. Frequently these lists include only the cabin passengers.
Usually it will be necessary to try to obtain passenger lists from the Australian end but Tuakiri | Identity, Level 2, Tūranga, does hold the Passenger lists, Victoria, Australia outwards to New Zealand, 1852 onwards microfiche.
There are 3 parts, covering the periods 1852-1860, 1861-1865 and 1866-1870. Each part includes an alphabetical list of passengers, an entry order list of passengers and ship information.
Contact Australian family history organisations to trace further Australia to New Zealand passenger lists.