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We have investigated the electron spin resonance (ESR) of the Ni45Cr5Mn37In13 Heusler alloy near the structural and magnetic phase transition temperatures. Ni45Cr5Mn37In13 is characterized by a first order magnetostructural (martensitic) transition (MST) with magneto-responsive properties such as magnetoresistance, Hall and magnetocaloric effects, etc., in the vicinity of the MST. Since the details and origins of these behaviors are not well understood, we used a technique beyond magnetometry, i.e., “microwave absorption”, to reveal new information. ESR studies of Ni45Cr5Mn37In13 shows that this compound is characterized by wide absorption spectra at temperatures greater than 250 K that depend on the angle of the magnetic field relative to the normal to the sample plate (α) and temperature (T). Two local maxima at about 5 and 6 kOe were detected for α close to zero degrees near the martensitic transition and Curie temperatures. The absorption spectra are discussed along with the results of the structural and magnetic studies.