A process for forming a thick-film resistor whose dimensions can be accurately obtained, thereby yielding a precise resistance value. The method includes providing on a substrate a photoimageable layer that preferably forms a permanent dielectric layer of a multilayer structure. An opening is photodefined in the surface of the photoimageable layer, and then overfilled with an electrically-resistive material to form a resistive mass having an excess portion that lies on the surface of the photoimageable layer surrounding the opening. Following curing which causes the surface of the resistive material to become recessed below the surface of the photoimageable layer, the excess portion of the resistive mass is removed, preferably by abrading or a similar operation, such that the lateral dimensions of the resistive mass are determined by the lateral dimensions of the opening in the photoimageable layer. Thereafter, subsequent processing is preformed to include the photoimageable layer as a permanent photoimageable layer of a circuit board, with the resistive mass and appropriate terminations forming a resistor in the permanent photoimageable layer.