A laminar fixation clamp has a body that utilizes a clam-shell style pivot controlled by a set screw, to grasp and attach to a spine rod, while receiving a laminar fixation band that can loop around a lamina of a vertebra in order to hold the laminar fixation clamp onto the vertebra. One form comprises a two-piece structure while another form comprises a single-piece structure. In each case, an upper and lower clamping structure situated at a front of the laminar fixation clamp, is received over and onto the spine rod, while a laminar fixation band is received through clamp. The set screw controls the amount of pivoting and thus the clamping force exerted onto the spine rod.