Materials with broad absorption bands are highly desirable for electromagnetic filtering and processing applications, especially if the absorption can be externally controlled. Here, a new class of broadband-absorption materials is introduced. Namely, layered metamagnets exhibit an electromagnetic excitation continuum in the magnetic-field-induced mixed ferro- and antiferromagnetic phase. Employing a series of complementary experimental techniques involving neutron scattering, muon spin relaxation, specific heat, ac and dc magnetization measurements, and electron magnetic resonance, a detailed magnetic phase diagram of Cu₃Bi(SeO₃)₂O₂Br is determined and it is found that the excitations in the mixed phase extend over at least ten decades of frequency. The results, which reveal a new dynamical aspect of the mixed phase in metamagnets, open up a novel approach to controllable microwave filtering. Controllable broadband microwave absorption is highly desired for improved electromagnetic shielding and superior signal processing. The absorption of the microwaves in an extremely wide frequency range is demonstrated in layered metamagnets. The effect is controlled by the external magnetic field and should be easily reproduced in artificial metamagnets, that is, magnetic multilayers, allowing a direct tuning of the functional properties.