We have developed a single-mode microwave reactor for continuous-flow synthesis with various methods of operation. This device measures the resonant frequency and modulates the oscillation frequency accordingly to maintain the maximum electric field intensity in the cavity. It can be operated either using constant applied irradiation power or using new programs which change the electric power (E-GRA) and change the flow rate (Fl-GRA), in order to rapidly screen various reaction conditions. As a model reaction, the Claisen rearrangement reaction of allyl 1-naphthyl ether 1 was rapidly optimized in this device, affording the desired product 2-allylnapthalen-1-ol 2 in high (91%) yield and up to 20 g/h productivity.