In the Auckland case, the wanted men were seen three weeks ago working in tandem, police said.
One placed a green sleeve device on the automatic teller machine while the other kept watch.
"The device looked exactly like the illuminated green slot into which customers insert their ATM cards," said Acting Inspector Hirone Waretini.
"This device sits over the top of the original green slot and contains an electronic chip that reads the details of the card as it enters the machine.
"The pair left this device for a couple of hours on the machine and intended to return to remove it. However, a customer using the ATM discovered the device when it came off in his hand as he removed his card. He promptly handed the device in to police," Mr Waretini said.
Police said the men were from Eastern Europe.
Both are thought to be in their late 20s to early 30s, of solid build, cleanshaven, with short dark hair.
Mr Waretini said police did not know where the men were and appealed for information about them, but asked that they not be directly told about the police interest in them.
Card-skimming has become popular in recent years.
Usually, a "skimming" device that looks as if it is part of the ATM is placed over the slot where the bank card is inserted. The bank card details are collected from the magnetic strip and a small camera above the keyboard records the PIN.
The stolen data can be transmitted wirelessly to the fraudsters, then emailed to associates overseas. The bank information is then sold to criminal groups around the world, which create counterfeit cards and withdraw the cash overseas.
In March, ANZ - after discovering fraudulent transactions made from Bulgaria - said fraudsters had been using the devices on its ATM machines.
"It does appear that these fraudsters have used hit-and-run tactics - placing devices on ATMs for a short time - to bypass our frequent checks," said a spokeswoman for the bank.
Protect yourself
Police say it is important that people are always vigilant around ATM machines and take precautions when entering their PIN number. If anyone has concerns that an ATM has been tampered with, or does not look right, they should contact their bank as soon as possible.