Decreasing the magnetic field signature of a naval vessel will reduce its susceptibility to detonating naval influence mines and the probability of a submarine being detected by underwater barriers and maritime patrol aircraft. Both passive and active techniques for reducing the magnetic signatures produced by a vessel's ferromagnetism, roll-induced eddy currents, corrosion-related sources, and stray fields are presented. Mathematical models of simple hull shapes are used to predict the levels of signature reduction that might be achieved through the use of alternate construction materials. Also, the process of demagnetizing a steel-hulled ship is presented, along with the operation of shaft-grounding systems, paints, and alternate configurations for power distribution cables. In addition, active signature reduction technologies are described, such as degaussing and deamping, which attempt to cancel the fields surrounding a surface ship or submarine rather than eliminate its source. Table of Contents: Introduction / Passive Magnetic Silencing Techniques / Active Signature Compensation / Summary