Adding to Tom's suggestion, you can go into the Display properties (Control Panel -> Display) and then to the Settings tab where your monitors are displayed. From there, you can reposition the monitors so that they are virtually vertically aligned as opposed to virtually horizontally aligned (moving the mouse up to the top of the screen past the first monitor enters the second monitor as opposed to moving it to the right on the other screen).
Not sure if this is what you're looking for specifically. As far as literally duplicating a window, I'm not sure if that's even technically possible within Windows. Mac OS X uses X.Org (as does most Linux distributions) which was a windowing system built around the network and terminals, so displaying windows on other systems (or duplicating a view, in this case) isn't a problem. That said, if the Webinar is available to be viewed within Linux, you could set up something akin to that.