We study the microwave-induced magnetization reversal in two systems, the microwave-driven nanomagnet (NM) and the NM coupled to a Josephson junction (JJ) under the microwave field (NM-JJ-MW). The frequency of the applied cosine chirp pulse changes nonlinearly with time to match the magnetization precession frequency. The coupling between the NM and JJ reduces the magnetization switching time as well as the optimal amplitude of the microwave field as a result of manipulating the magnetization via Josephson-to-magnetic energy ratio G. The reversal effect in NM-JJ-MW is sufficiently robust against changes in pulse amplitude and duration. In this system, the increase of G decreases the possibility of the non-reversing magnetic response as the Gilbert damping increases without further increase in the external microwave field. We also discuss the magnetic response of the NM driven by the ac field of two JJs in which the time-dependent frequency is controlled by the voltage across the junctions. Our results provide a controllable scheme of magnetization reversal that might help to realize fast memory devices.