Find a Grave has 2188 cemeteries listed for New Zealand. Many of these have memorials with a percentage photographed. For example, Addington Cemetery has 10,361 memorials at the time of writing and 11% have been photographed.
Selecting a cemetery will provide you with an option to search the memorials. This is done by first and last names. It also provides information on the cemetery such as an address, map and photographs.
Selecting a memorial result provides information on the deceased. It may include full name, date of death, burial plot, parents and a photo.