RBS Group - which represents RBS and NatWest - has said cases of customers being "out of pocket" due to the recent card payment problems will be considered on an individual basis.
Customers are asked to call their bank or visit a branch to discuss the matter with staff.
A spokesman for RBS said: "We are committed to putting this right."
- NatWest customers should call: 0800 151 0404
- RBS customers should call: 0800 151 0405