The so-called metamagnetic shape memory alloys transform from a ferromagnetic austenite into a weak magnetic martensitic phase, thus the application of a magnetic field, stabilizing the high magnetization phase, can induce the reverse martensitic transformation. Moreover, the martensitic transformation itself becomes arrested as its temperature range is lowered by the application of high enough magnetic fields. In this work the effect of the magnetic field on a Ni-Mn-In-Co metamagnetic shape memory has been studied by SQUID magnetometry. The arrest of the transformation produced by the field results in metastable states, whose evolution when the field is removed or reduced, follows logarithmic time dependence. The observed behavior is interpreted in terms of the magnetic contribution to the total entropy change associated with the magnetostructural transformation.