The charities are taking part in a month-long trial of the DonorPoint machine, which resembles a cashpoint and allows charities to take credit and debit card donations from unattended locations 24 hours a day.
The National Trust installed the machines at its Arlington Court estate in Devon and its Greenway woodland garden site near Dartmouth last month.
The National Museum of Wales will be following suit this week and several Cathedrals are also taking part in trials.
"We have had the machine for two weeks now and are delighted with it," said David Burrows, administrator at Chester Cathedral, the first in the country to accept credit card donations. "The average donation from DonorPoint is £5 compared with just 30p for the traditional collection box."
The machine also helps charities claim GiftAid. It asks donors to enter a postcode and house number and then combines this information with details from the credit card to produce a spreadsheet to be used for GiftAid applications.
"DonorPoint is producing some positive results," said Brad Burton, head of marketing at Wild Yeast, the company that designed the machine along with car park ticket machine specialists Minerva and Blick. "I think it will prove to be a great asset for charities by tapping into today's credit card culture."
The machines use wireless technology developed by mobile phone companies to debit the donor's credit card, which means that they are portable and are easy for charities to install because there is no need to connect them to a telephone line or modem.