The substantial undisclosed damages, in addition to legal costs, were announced in the High Court in settlement of libel actions brought by Brian and Margaret Allen and their company, D Allen and Sons (Butchers) Ltd of Spalding, Lincolnshire.
Mr Justice Drake was told the Allens were away on holiday in the United States at the time the cheques were dishonoured by the bank at the end of 1983.
Michael Tugendhat QC said a number of cheques issued by the Allens' company to suppliers were returned unpaid by the bank. The suppliers remained unpaid for the time it took Mr and Mrs Allen to return from holiday and sort out the matter.
The couple launched libel proceedings to quash any doubt about their financial soundness and creditworthiness. Lloyds acknowledged that the cheques should have been met and regretted that they were not.
The bank apologised for what happened and said it was as a result of a misunderstanding. It agreed to compensate the Allens for damage and embarrassment.
Afterwards Mr Allen said: 'It is the end of a chapter today. It has taken a long time to get here. However, we have got everything we wanted. The main thing we wanted was an apology.'
His solicitor, James Sutton, said it was rare but not unique for a bank to be sued for libel because it refused to honour cheques.