Maybe throttle the number of advanced functins or calculations unregistered users are allowed to do per day (or session, or other time period) and have a countdown/tracker displaying the number they have remaining along with a link to register.

Buy the desktop version, get unlimited access to the web version.

Put an identifier cookie on their machine and display the number of calculations performed over all time along with a link to the purchase. You know, guilt.

Maybe have a few of the more esoteric but ridiculously useful functions disabled and only enabled either in the pro or just by viewing a nag screen - click sin and get a popup (the first time this session only) that says "We're glad you like this, hey there's a free version). Only nag them a very small percentage of the time, but every now and then nudge them a bit.