We present a numerical simulation method to simulate time-dependent slip-flow for values of Knudsen number less than 0.1 in complex micro-domains encountered in micro-devices such as micro-capillaries, micro-valves, and micro-bearings. The present method is an extension of the spectral element technique which has been applied succesfully in the past for simulations of incompressible flows governed by the Navier-Stokes equations. In the first part, validation of the method is obtained by comparison of the numerical simulation results in simple prototype flows (e.g. Poiseuille and Couette slip-flows) with analytical solutions. Reduction of pressure drop in micro-channels, reported in similar experimental studies, is investigated using slip-flow theory and simulations. In the second part, we consider model flows through complex geometries such as three-dimensional ducts, micro-cavities and slip-flow past a circular cylinder. The effect of slip-flow on skin friction reduction and associated increase in mass flow rate as well as the variation of the normal stresses is investigated as a function of Kn udsen number. Our results demonstrate that a stand alone simulation approach, free of numerical artifacts, can be employed to efficiently predict momentum and energy transport in micro-devices.