You could use a similar method to that of a digitizer.

under the board you could set up a grid of wires, there is a common termination for each axis.
Each wire runs accros the board moves up one grid space and back to the side, this forms a row of long thin loops on one axis. You end up with a common and 'n' connections down one side for one axis. 
Do the same for the other axis. 

Each object would need a coil of wire and a capacitor minimum. ( better a coil, PIC & battery.  This would allow individual objects to be identified through addressing the object to locate).

The number of wires ( loops) in the grid could be adjusted to suit the resolution required.
With the passive objects, a loop on each axis may need to be used simultaniously to identify an object location.( ie one as a transmitter and the other as an antenna.

With active objects, first broadcast the objects address, then lissen on each loop one at a time to find the strongest signal & therefor an objects location. In a digitizer more than one loop gets the signal & the ratio of the signal levels are used to give a finner resolution than the grid.