Well if someone has lied about their age to get on a forum and are clearly under age, they should be removed by the admin. Simple as that.
Its not always as simple as that sadly
The registration process needs a DOB to complete and potential members can always lie about their age, there is nothing available to admins that can be used to check the DOB given
However, the posting style and behaviour of a member can and usually does give the underage member away....not always very quickly, as when new they tend to be ultra polite and make all the right responses. As time goes by that "nice" behaviour tends to break down and the child starts to emerge, eventually the child causes too much disruption due to arguments or rude responses or just basic immaturity in their posts and that will inevitably lead to a ban...especially if they have been contacted by a staffmember and warned about the way they are behaving
Of course there are exceptions, where an underage member does behave in a mature way throughout, and although they are breaking COPPA rules, they can be given a chance by virtue of that mature behaviour
Under 13's do not always have a very good concept of how to behave and can easily act out in what can only be described as kindergarten behaviour when they do not get their own way or they get a response they do not like.
Being an admin or mod on a site like this is extremely hard sometimes but when you have a disruptive member of any age you have to place the welfare of the forum as a whole over that one person. When I was an admin/site builder, I had the last word on bans and I had my staff document everything that person had done, we discussed it behind the scenes, we had a 3 strikes and out policy....we gave people every chance to behave in an appropriate manner but inevitably you have to act and on my sites that was down to me as admin and even when you have the devil incarnate messing up on your forum, its still not a pleasant task having to ban anyone.....but its part and parcel of the territory sadly.