In quantum illumination entangled light is employed to enhance the detection accuracy of an object when compared with the best classical protocol. On the other hand, cloaking is a stealth technology based on covering a target with a material deflecting the light around the object to avoid its detection. Here, we propose a quantum illumination protocol especially adapted to quantum microwave technology. This protocol seizes the phase-shift induced by some cloaking techniques, such as scattering reduction, allowing for a 3 dB improvement in the detection of a cloaked target. The method can also be employed for the detection of a phase-shift in bright environments in different frequency regimes. Finally, we study the minimal efficiency required by the photocounter for which the quantum illumination protocol still shows a gain with respect to the classical protocol.