Neutron diffraction measurements, performed in presence of an external magnetic field, have been used to show structural evidence for the kinetic arrest of the first-order phase transition from (i) the high temperature austenite phase to the low temperature martensite phase in the magnetic shape memory alloy Ni37Co11Mn42.5Sn9.5, (ii) the higher temperature ferromagnetic phase to the lower temperature antiferromagnetic phase in the half-doped charge ordered compound La0.5Ca0.5MnO3 and (iii) the formation of a glass-like arrested state (GLAS). The CHUF (cooling and heating under unequal fields) protocol has been used to establish phase coexistence of metastable and equilibrium states of GLAS and also to demonstrate the devitrification of the arrested metastable states in the neutron diffraction patterns. We also explore the field-temperature (H,T) phase diagram for the two compounds, which depicts the kinetic arrest line TK(H). TK is seen to increase as H increases.