In situations where the errors can build up badly, e.g. long-duration orbital calculations, there's a tendency for the energy of the system not to be conserved by the usual DE integration methods, e.g. predictor-corrector or Stoer-Bulirsch. Those sorts of calculations are now done using what are called 'symplectic integrators', which inherently conserve energy to the level of roundoff. It's probably quite possible to do the same sort of thing for charge conservation in circuit simulation, but it would seem to be unnecessary, since almost all useful circuits have current flowing in and out of them.
Cheers,
Phil Hobbs