An electrically conductive sidewall for an electromagnetic transducer having a magnetoresistive sensor is formed as a layer oriented substantially perpendicular to other layers of the sensor, and is used as a mask for defining the width of the sensor. This allows the sensor to be made much thinner than conventional sensors, providing higher resolution in a track width direction. The sidewall can be nonmagnetic, serving as a spacer between the magnetic sensor layers and an adjacent magnetic shield without the need for a protective cap to guard against damage from polishing and wet etching. Alternatively, the sidewall can be magnetic, serving as an extension of the shield. In either case, the sidewall reduces the effective length of the sensor for linear resolution, sharpening the focus of the sensor and increasing linear density. Also reduced is the tolerance for error in sensor width and length. The combination of increased resolution in track width and track length directions provides a large increase in areal resolution, such that sensors in accordance with the present invention may be able to resolve signals at a density exceeding a terabit per square inch. A correspondingly narrow pole-tip for an inductive transducer that may be employed in conjunction with the magnetoresistive sensor is also disclosed.