Methods for recovery of at least one alcohol from dilute aqueous alcohol feed streams are described. The methods include steps of a) providing a source of a dilute aqueous alcohol feed stream including at least one alcohol; b) substantially removing any solids from the dilute aqueous alcohol feed stream to form a feed stream substantially devoid of solids; c) circulating the feed stream substantially devoid of solids through a liquid-liquid extraction system having multiple equilibrium stages; d) recovering a raffinate phase substantially depleted in the at least one alcohol and an extract phase substantially enriched in the at least one alcohol; e) passing the extract phase to a recovery system wherein the extract phase is subjected to microwave radiation; f) recovering the volatilized product; and g) recycling the solvent to the liquid-liquid extraction system. The microwave radiation substantially heats the alcohol but not the solvent to form a volatilized product of substantially pure alcohol. The methods further include optional steps of removing any residual water from the substantially pure alcohol product to form a fuel-grade alcohol. The liquid-liquid extraction system can be a hydrophobic, microporous membrane extraction system having a plurality of hollow fibers.