A continuation of the "weird" stuff with super-conductors...
We have a stack of super-conductor sheets inside a solenoid. The magnetic field generated by the solenoid is greater than the critical field of the sheets by a little. We move one sheet out until the field it's in is less than the critical field.
The sheet gets shot out by repulsive forces due to Meissner effect. Now we keep the sheet thickness the same, and increase everything else by a factor k (except the B field which is by factor 1). Then the weight of the sheet increases as k2, but the energy it gains increases as k3, so there is an energy density improvement by k. So we can get unlimited energy density! Provided we can make large objects to very high precision. The explanation being extra field to the Maxwell Equations in the normal-to-Meissner transition.