Using Electricity and Magnetism to Lift non-ferromagnetic Copper Pennies
The "copper-lifting magnet" is a cool old physics demonstration.  It's a method to lift aluminum or copper plates.   It should work on pennies, in theory.  But probably it will require water-cooling, and the penny will heat up fast, since the principle is much like an induction furnace.

Here's the secret:   make a laminated-core AC electromagnet.  Then bolt a thick ring of aluminum or copper onto the end.  When you turn on the coil, the metal ring will have a huge AC short-ciruit current, like a shorted transformer winding.  It will try to fly off the end of the electromagnet core (by inductive repulsion.)   But if it remains attached, and if you put the solid ring against a metal plate, the ring attracts the metal plate.

How?   The AC electromagnet induces closed circles of current in both the metal ring and the metal plate.  The currents are in the same direction.  So, although the electromagnet will try to repel both of them, the two metal objects will attract each other.   So, permanently affix the metal ring to the end of the AC electromagnet.  Like magic you have a "non-ferrous magnetic attractor."

Unfortunately the whole process involves quite large currents, kiloamperes, and for a small electromagnet (lifting a small metal object,) I think the problem gets worse.