Paul Attwater, 65, and Iris Attwater, 66, from Ketley in Telford, smuggled prohibited aircraft parts to Alexander George in Malaysia from their company Pairs Aviation.
But the couple were handed suspended sentences after Mr Attwater insisted he had no idea the 'nuts and bolts' he was exporting had a military application.
George, who is due to be sentenced next month, acted as a broker between the couple and Iranian buyers.
He held substantial contracts to source and supply Iranian aviation firms with parts and components for planes and helicopters through companies he owned in Malaysia and Dubai, Southwark Crown Court heard.
George, 76, sourced parts from Pairs Aviation which were then exported by the Attwaters via a Dutch shipping company and on to Iran through a network of companies in the Far East.
The aircraft parts could have been used in Iran's nuclear programme - an undertaking that has come under increasing scrutiny following the cessation of the Iran nuclear deal by President Trump.
The Attwaters were well aware of the need for a licence to export some of their products after border officials impounded their goods.
But the couple continued to deal with George, sending him the same parts that had been returned by Customs via a forwarding house in the Netherlands.
Judge Michael Grieve QC said: "The fact that you were, in effect, groomed by Mr George I accept - he deceived you.
"I do not, for one moment, think that either of you are bad people. You have, in my view, been very, very naive."
Prosecutor Edmond Burge told the court: "Mr Attwater pleaded guilty at the close of all of the evidence following legal argument as to the status of his defence.
"Mrs Attwater falls into a slightly different position because she maintained her not guilty plea and was convicted by the jury.
"We cannot show that the Attwaters know that the final destination of these goods was Iran."
George Hepburne-Scott, defending Mr Attwater, said: "This, I submit, is a truly exceptional case.
"Mr Attwater is 65 years old, he is an exemplary citizen.
"He genuinely did not believe that these items could have a military application... these were nuts and bolts. He has also been completely open with the authorities.
"He has been extremely naive."
Judge Grieve told the Attwaters: "My ruling left you no defence as a point of law.
"The jury convicted you (Mrs Attwater) unanimously after a short deliberation," he said, addressing Mrs Attwater.
Weapons of mass destruction
The judge explained that in 2009, customs officials blocked the exports of some of the goods which required a licence 'due to concerns about the production of weapons of mass destruction in Iran.'
"Despite undertaking not to export these goods you proceeded again to send them out to Malaysia.
"These export controls might be confusing but they are there for a very good reason.
"That ultimate risk is one with potentially very serious humanitarian consequences. Such a consequence included use against others in nuclear weapons."
Mr Attwater agreed to sign a basis of plea prior to his formal guilty plea, in which he said: "I did not know or believe that goods or aircraft components would be shipped to Iran.
"I did not think there was even the remotest opportunity of these good ending up in a nuclear weapons program."
George, of Long Ashton, Bristol, denied two counts of being knowingly concerned in the supply or delivery of controlled goods to an embargoed destination but was found guilty by a jury.
Mr Attwater admitted being knowingly concerned in the exportation of goods with intent to evade prohibition or restriction
Mrs Attwater denied but was convicted of the charge.
They were both sentenced to six months jail suspended for 12 months and barred from being company directors for the next six years.
Proceedings against George's wife, Ruth, 74, were dropped after it ruled she had no case to answer.