One illustrative integrated circuit (IC) product disclosed herein includes an MRAM cell, the MRAM cell having an outer perimeter, wherein the MRAM cell comprises a bottom electrode, a top electrode and an MTJ (Magnetic Tunnel Junction) element positioned above the bottom electrode and below the top electrode. In this example, the IC product also includes an insulating material positioned around the outer perimeter of the MRAM cell and a conductive sidewall spacer comprised of a metal-containing shielding material positioned around the outer perimeter of the MRAM cell, wherein the insulating material is positioned between the conductive sidewall spacer and the MRAM cell.