Customers affected by NatWest's IT meltdown have been urged to keep a record of what happened and how they were left out of pocket.
The Financial Ombudsman Service (FOS) said banks are obliged to return their clients to the position they would have been in had the problem not existed.
Customers can turn to the FOS if they cannot resolve a complaint with their bank.
A spokeswoman said that each case would be looked at individually by the FOS if complaints were made to it.
She cautioned that complaints involving "consequential losses", such as someone missing a flight because they could not access their money, may not necessarily be straightforward.
But she said that often when similar incidents have happened and many people have been affected, the ombudsman only ends up seeing a few complaints from people as the bank has largely cleared them up.
Asked during an interview with ITV News about the possibility of compensation for customers, Susan Allen, customer services director for RBS-Natwest Retail, said anyone who has incurred extra charges as a result of the problems should contact the bank concerned.
She assured customers: "We will make sure that nobody is out of pocket as a result of this."
A spokeswoman for the Financial Services Authority, which regulates the banks, said: "We are aware of the technical problems RBS-NatWest is having.
"They have kept us fully informed and are working hard to resolve the problem as quickly as possible."