Some sites give you the ability to pre-move during live games, where you can preselect a legal move while it's still your opponent's turn. For example, let's say you know your opponent will capture a piece; while waiting for that to happen, you preselect a piece and move it to a square which will instant happen as soon as it is your turn. Doing so saves save time on the clock and speeds up live games.
This would be a nice feature on RHP. I'll PM Russ as site that has this feature.
I knew this request was coming, so it was always in the back of my mind when developing the new board code (which is used for live)
I can't offer an approximation of when it will be available though without diving in to the code again. (Definitely one of those changes that could be at either extreme of effort!)
I will add it to the "TODO" list on the whiteboard of shame, so it will be addressed relatively soon.