An analytical slip-flow model based on second-order boundary conditions was proposed for gaseous flow in rectangular microchannels. An experimental setup has been designed for the measurement of gaseous micro flow rates under controlled temperature and pressure conditions. Data relative to nitrogen and helium flows through rectangular microchannels, from 4.5 to 0.5 mum in depth and with aspect ratios from 1-9%, are presented and analyzed. A method is proposed to eliminate the main source of uncertainty, which is the imprecision when measuring the dimensions of the microchannel cross-section. It is shown that in rectangular microchannels, the proposed second-order model is valid for Knudsen numbers up to about 0.25, whereas the first-order model is no longer accurate for values higher than 0.05. The best fit is found for a tangential momentum accommodation coefficient sigma = 0.93, both with helium and nitrogen.