Two people were scammed out of almost £13,000 last weekend, the PSNI has said.
One of the victims had nearly £10,000 taken from their bank account after they gave their bank details over the phone, while the other lost £2,500.
Both of them were scammed by people claiming to be from BT within a day of each other.
The scams happened on Friday and Saturday in counties Armagh and Tyrone.
The second victim was kept on the phone for about three hours and persuaded to download software, which resulted in the victim being swindled out their money.
'Scammers will use any tactic'
Chief Superintendent Simon Walls has called on families to stay alert and for people not to give out financial details over the phone.
"I want to appeal to family members to do all they can to let their loved ones know, especially those who are older and vulnerable, never to give out any kind of financial details over the phone or to download software during a call unless they are 110% sure it is safe to do so," he said.
"Scammers are creative and will do whatever they can to con people out of money. They don't care who their victim is, they just want the money and will employ whatever tactic is necessary."