Scotland's national bullying charity Respectme has told families replying to offensive messages on social networking sites or other online messaging services to exert extreme caution.
The move comes after a dramatic rise in cyberbullying over the past few years as increasing numbers of pupils who own smartphones and tablet computers take them to school.
Figures published in 2013 show Scottish schools recorded more than 500 incidents in the previous three years, although the true figure will be significantly higher because many councils were unable to provide statistics.
Examples included children as young as eight verbally abusing each other on social media sites and pupils exchanging insults over X-box console messaging services. There were also incidents of children filming bullying.
Parents often find such incidents difficult to deal with because they are unfamiliar with the technology being used.
The new guidance from Respectme suggests parents should examine any bullying messages, posts or pictures that their children have received.
Any of these messages or pictures that could be construed as illegal should be kept along with dates, times, email addresses and taken to the police.
On the issue of contacting bullies direct the advice states: "You might want to reply to these messages, but be careful not to respond in a manner which could be seen as threatening or harassing.
"It may be enough to respond saying that you are an adult and that the messages they are sending are hurtful, causing you and the young person concern, it could be against the law and that they should stop sending them."
Brian Donnelly, director of Respectme, said he was aware of some instances where parents had over-reacted to cyberbullying.
He said: "We accept there is an immediate emotional response in parents, but that can trigger an over-reaction and can lead to unintended consequences.
"Any suggestion of an adult threatening a child would be extremely serious and it is much better to calm down before responding. We would also suggest that if the child does not want their family to get involved then that advice should be followed because it is about giving them back some power."
Eileen Prior, executive director of the Scottish Parent Teacher Council, described the issue as "very tricky territory".
"If parents are considering replying to online bullies then they would have to be extremely careful," she said.
"When we are contacted by parents on issues such as this we encourage parents to have a dialogue with their children first to establish what has happened.
"Clearly the age of the child or young person is a significant factor in how parents and young people address online bullying and what steps they should take."
Earlier this month, the Scottish Government announced new research to look at young people's experiences of online bullying.
Speaking then, Minister for Learning Alasdair Allan said: "Online bullying is unacceptable, but it does present new challenges to the traditional ways we would recommend dealing with the situation. Whether we like it or not, many young people do not consider online insults to be the same as bullying in person and we must be clear that online abuse can be just as devastating as any other form of attack."