An absence of theoretical justification for the magnitude of resistivity is one of the major limitations of large-scale simulations of magnetic reconnection in collisionless magnetospheric plasma. We took advantage of the results of recent progress in kinetic modeling of collisionless dissipation in the vicinity of the magnetically neutral X point aiming to find ways to represent small-scale kinetic effects in large-scale models. The study was based on a combination of hybrid and particle methods and on analytical analysis. A comprehensive hybrid simulation code which incorporates the leading terms in electron dynamics responsible for breaking the frozen magnetic flux constraint (electron bulk flow inertia and nongyrotropic pressure effects) was utilized. The results of the comprehensive hybrid model were found to be in excellent quantitative agreement with the results of full particle simulations with similar setups. Both simulations demonstrated that the actual reconnection electric field is determined primarily by kinetic quasi-viscous effects and less by electron bulk flow inertia. An analytical expression for the quasi-viscous reconnection electric field averaged over the nongyrotropic region was obtained. Similar behavior of the evaluated quasi-viscous electric field and actual reconnection electric field taken from the simulations was demonstrated. Conventional hybrid simulations with simple nongyrotropic corrections to the electric field where also performed. The model was further reduced for utilization in MHD models. Analytical expressions for the time evolution of the reconnected flux evaluated from the MHD model modified by nongyrotropic corrections appeared to be in very good agreement with the results of comprehensive kinetic simulations. The evaluated averaged quasi-viscous electric field can be substituted into large-scale simulation models. ¿ 2000 American Geophysical Union