One of the questions I am constantly asked in my new role of online tournament organiser is "How do you deal with cheating?" My quick answer is "I don't" but the real answer is a little more involved than that.
At the moment the events I organise are small-ish events, with no more than 30 players. I also generally know all the players in the events, and those I don't, I ask them to clearly identify who they are in real life. The reasoning for this is that I believe players are less likely to misbehave in smaller social settings if they now everyone else knows who they are. Secondly, the platforms for online chess also have their own ant-cheating systems built in, which provides both a deterrent, and a system for sanctioning players.
As a result there haven't been anything I would describe as obvious cheating in anything I have organised, although I know of at least one player who did get sanctioned by the site these events run on (NB I am not privy to the reasons why this happened).
However it can still go somewhat wrong for other tournament organisers, as discovered by the Melbourne Chess Club. The MCC run a Saturday Allegro Competition (modelled after Street Chess), and have also moved it online. They also decided to "go big" with yesterdays event, attracting a field of 128 players. In the first round, one of the top seeds was beaten by an unrated/unknown player. While this may not have been a huge surprise in real life, in online chess it was enough to reverse the result and exclude the winner from the rest of the tournament. I believe there was a copy of the game that was briefly online, but has also now been removed from the tournament website.
At this time this is all the information I have seen on this matter, but I assume the organisers had more evidence than simply "this result doesn't seem right". There is a line between playing out of your skin and playing with electronic help, but sometimes organisers find it difficult to put a player on the correct side of it. Hopefully, as players and organisers gain more experience with these events, such incidents will diminish.