What kind of game is it?
Is it possible to keep the 2 simulations entirely in sync?
If you start the 2 instances of the simulation in exactly the same state, and update with a fixed timestep, then they should remain synchronized.
But when you do anything to a physics object, you send a message to all clients telling them what to do and on which frame.
So if you were making something like 'Worms' or 'Angry Birds', and the player launched a projectile on frame 1000, you'd send a message saying 'on frame 1000+N' we're going to spawn a physics object with these parameters.
Of course, this will add input lag. And you need some way to ensure that no player will get too far ahead to respond to messages on the correct frame. Maybe a 5-10Hz 'clock' message, telling all clients 'you may advance your simulation to frame N, but no further'.
(I believe that this is how online RTS games work, where it would not be practical to send the positions and states of several hundred units every update, and where a fraction of a second's lag between giving an order and the unit executing it is acceptable)