We have used empirical models for electric potentials and the magnetic fields both in space and on the ground to obtain maps of the height-integrated Pedersen and Hall ionospheric conductivities at high latitudes. This calculation required use of both "curl-free" and "divergencefree" components of the ionospheric currents, with the former obtained from magnetic fields that are used in a model of the field-aligned currents. The second component is from the equivalent current, usually associated with Hall currents, derived from the ground-level magnetic field. Conductances were calculated for varying combinations of the interplanetary magnetic field (IMF) magnitude and orientation angle, as well as the dipole tilt angle. The results show that reversing the sign of the Y component of the IMF produces substantially different conductivity patterns. The Hall conductivities are largest on the dawn side in the upward, Region 2 field-aligned currents. Low electric field strengths in the Harang discontinuity lead to inconclusive results near midnight. Calculations of the Joule heating, obtained from the electric field and both components of the ionospheric current, are compared with the Poynting flux in space. The maps show some differences, while their integrated totals match to within 1 %. Some of the Poynting flux that enters the polar cap is dissipated as Joule heating within the auroral ovals, where the conductivity is greater.