  The tunneling rate t_v of a vortex between two pinning sites (of strength V
separated by d) is computed using the Bogoliubov expansion of vortex
wavefunctions overlap. For BCS vortices, tunneling is suppressed beyond a few
Fermi wavelengths. For Bose condensates, t_v = V exp(- pi n_s d^2/2), where n_s
is the boson density. The analogy between vortex hopping in a superconducting
film and 2D electrons in a perpendicular magnetic field is exploited. We derive
the variable range hopping temperature, below which vortex tunneling
contributes to magneto-resistance. Using the 'Quantum Hall Insulator' analogy
we argue that the -Hall conductivity- (rather than the inverse Hall
resistivity) measures the effective carrier density in domains of mobile
vortices.
  Details of vortex wavefunctions and overlap calculations, and a general
derivation of the Magnus coefficient for any wavefunction on the sphere, are
provided in appendices.
