Some Yorkshire Bank and Clydesdale Bank customers were unable to use their debit cards twice in three days following computer problems.
The banks, part of the same group, were transferring their systems operations to an external contractor when the first problems arose on Sunday morning.
This was followed by an hour-long interruption for some customers at 1200 GMT on Tuesday.
The banking group has apologised to customers whose cards were declined.
A spokesman said that the banks would take a "sympathetic approach" to anyone who suffered financial losses as a result of the problem.
Anyone affected in this way can contact their bank or go into their local branch.
The problems, which saw some debit cards declined from 1030 GMT on Sunday until first thing on Monday, primarily affected Yorkshire Bank customers, the spokesman said.