Ivor Gifford from Abertillery sent explicit messages to fake profiles set up by a group called The Hunted One, which claims to "hunt sexual predators".
He claimed he believed everyone on the site was over 18, but a jury at Newport Crown Court found him guilty.
Sentencing will take place on 2 June.
The court heard two profiles 'Jessie' and 'Jodie' were contacted by Gifford.
He repeatedly sent messages and made comments which were of a sexual nature despite being told several times by those behind the profiles they were 11 and 12.
Owen Williams, prosecuting, said: "He was persistent in his attempts. In over 100 pages of messages, you will see that the vast majority refer to a sexual act.
"Mr Gifford graphically describes sexual acts. He sent images of himself naked."
The court heard the chat logs described Mr Gifford asking if the person he was speaking to had reached puberty yet, and if she would "dress sexy" if they met.
Mr Williams continued: "He then went a stage further, having groomed online he made arrangements to meet her.
"Directing a child, who doesn't know how to get from Cardiff to Abertillery, how to get a bus then a train."
Two members of The Hunted One confronted Gifford at Llanhilleth train station, where he had arranged to meet his online contact.
The police were then called and Gifford was arrested.
He had denied inciting a child under 13 to engage in sexual activity and a charge of online grooming but a jury deliberated for around an hour before finding him guilty.
Det Supt Leanne Brustad, head of public protection for Gwent Police, said while officers relied on members of the public to detect crime, it was important not to cross the line into vigilantism.
"Revealing the identity of suspected paedophiles gives the suspect the opportunity to destroy evidence before the police can investigate them," she said.
"It also leads to people who have been identified going missing or raising concerns for their safety.
"This can divert significant resources into protecting suspects, which would be better invested in investigating and, where there is evidence, prosecuting them."
A 92-year-old man has been found guilty of using a chatroom to incite what he believed were 11 and 12-year-old girls to engage in sexual activity.