Metamagnets, which exhibit a transition from a low-magnetization to a high-magnetization state induced by the applied magnetic field, have recently been highlighted as promising materials for controllable broadband absorption. Here we show results of a multifrequency electron spin resonance (ESR) investigation of the Cu₃Bi(SeO₃)₂O₂Br planar metamagnet on the kagome lattice. Its mixed antiferromagnetic/ferromagnetic phase is stabilized in a finite range of applied fields around 0.8 T at low temperatures and is characterized by enhanced microwave absorption. The absorption signal is non-resonant and its boundaries correspond to two critical fields that determine the mixed phase. With decreasing temperature these increase like the sublattice magnetization of the antiferromagnetic phase and show no frequency dependence between 100 and 480 GHz. On the contrary, we find that the critical fields depend on the magnetic-field sweeping direction. In particular, the higher critical field, which corresponds to the transition from the mixed to the ferromagnetic phase, shows a pronounced hysteresis effect, while such a hysteresis is absent for the lower critical field. The observed hysteresis is enhanced at lower temperatures, which suggests that thermal fluctuations play an important role in destabilizing the highly absorbing mixed phase.