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Here, we present a study of the influence of microstructure on the magnetic properties of polycrystalline samples of the La1.5⁢Sr0.5⁢CoMnO6 double perovskite, with primary attention to the spontaneous exchange bias effect, a fascinating recently discovered phenomena for which some materials exhibit unidirectional magnetic anisotropy after being cooled in zero magnetic fields. By sintering La1.5⁢Sr0.5⁢CoMnO6 at different temperatures, we obtained samples with distinct average grain sizes, ranging from 1.54–6.65 µ⁢m. A detailed investigation of the material's structural, morphologic, electronic, and magnetic properties using x-ray powder diffraction, powder neutron diffraction, x-ray absorption near edge structure spectroscopy, scanning electron microscopy, and ac and dc magnetometry has revealed a systematic enhancement of the exchange bias effect with increasing the average grain size. This evolution is discussed in terms of changes in the material's porosity and grain morphology and its influence on the exchange couplings at the magnetic interfaces.