Abstract: The generation of volatiles from liquid or solid materials is enhanced and accelerated by exposure to microwave radiation. Normally the energy transfer is effected preferentially toward the liquid or solid materials over the generated gaseous volatiles. Sufficient energy is provided at a selected rate that enhances the generation of volatiles to effect removal as vapor or to produce a pressurized vapor phase. Flow-through separations from a matrix having a microwave-absorbing liquid component are conducted by exposing to microwave radiation to vaporize this component and processing the vapor either by flowing through a selective permeable membrane, or by enclosing the vapor and matrix in a confined space and flowing matrix through a selected separation medium, and recovering residual matrix. These separations are particularly useful in analysis contexts.