Gas microflows are encountered in many applications of Micro-Electro-Mechanical Systems (MEMS). Computational modeling and simulation can provide an effective predictive capability for heat and momentum transfer in microscales as well as means of evaluating the performance of a new microdevice before hardware fabrication. In this article, we present models and a computational methodology for simulating gas microflows in the slip-flow regime for which the Knudsen number is less than 0.3. The formulation is based on the classical Maxwell/Smoluchowski boundary conditions that allow partial slip at the wall. We first modify a high-order slip boundary condition we developed in previous work so that it can be easily implemented to provide enhanced numerical stability. We also extend a previous formulation for incompressible flows to include compressibility effects which are primarily responsible for the nonlinear pressure distribution in micro-channel flows. The focus of the paper is on the competing effects of compressibility and rarefaction in internal flows in long channels. Several simulation results are presented and comparisons are provided with available experimental data. A specific set of benchmark experiments is proposed to systematically study compressibility, rarefaction and viscous heating in microscales in order to provide validation to the numerical models and the slip-flow theory in general as well as to establish absolute standards in this relatively young field of fluid mechanics.