.Lincolnshire Police say incidents were reported on Wednesday in Boston and in the Wolds.
And they warn people to be on their guard, as they are expecting more attempts.
The fraud involves a call from the bank or the police asking the would-be victim to hand their cash or card over to a courier who would visit their home.
A spokesperson for the force said: “Experience shows that when offenders start calling here, attempting to steal from our residents, they hit us hard.
“We had two reports yesterday, one in Boston and one in the Wolds and we expect more.
“Thankfully, in part due to local media and residents support for our awareness building, these two potential victims didn't fall for it.
“Please share this information with your friends, relatives and neighbours and in doing so, help others arm themselves with this knowledge so they don't fall for it either.”
Courier fraud is when criminals call people impersonating banks or the police in order to convince them to hand over their cash, bank cards, or high value items, to a courier that’s been sent to their home.
Police say an increasingly popular tactic is for criminals to tell the unsuspecting victim to purchase high value items such as gold coins, watches and gold bullion.
The spokesperson for the force said: “Your bank or the police will never call you to ask you to verify your personal details or PIN by phone or offer to pick up your card by courier.
“Hang up, use a different phone if you have one (these criminals keep the line open whilst you dial, misleading you into thinking you are talking to your bank) and call your bank on a number you know to be genuine.
“Your bank or the police will not contact you out of the blue to participate in an investigation in which you need to withdraw money from your bank or to purchase high value goods, such as watches, gold coins, jewellery or gold bullion.
“And your bank will never send a courier to your home to collect your card, PIN, or other valuables; any requests to do so are a scam.”
They said that if anyone has any doubts at all, they should call the police on 101 and report the incident. If a courier is at their door, they should call the police on 999.