We present a technique of phase separation suitable for microfluidic systems and demonstrate its efficient integration with a microfluidic optical cell for performing real-time spectrometric measurements on one specific phase from a mixture. We demonstrate that efficient and robust phase separation based on capillarity is possible within a microfluidic chip using either microfabricated capillary channels in polydimethylsiloxane (PDMS) or oil-wet fluoropolymer membranes, allowing for extraction of either the continuous or of the dispersed phases from a multiphase mixture. We analyze the dependence of phase separation efficiency on the operating parameters of the device and observe the presence of a hysteresis cycle during pressure sweeps above a water breakthrough pressure (P(b)); we also observe and analyze the reversibility of the oil-wet state of the membrane upon pressure reduction below a reset pressure (P(r) < P(b)). We test the capillary separation method extensively with several types of organic/water mixtures and emulsions and derive criteria for design and operation of a robust microfluidic capillary separator. As an example of monitoring application we describe the design and manufacturing of a microfluidic spectrometer cell optimized for fast response time, which was used to analyze the oil extracted from an oil/water emulsion using a capillary separator. The complete separator-sensor system is characterized in terms of response and cleanup times to instantaneous changes in the dye concentration of the phase of interest.