A cable clamp assembly and a cable clamp method for a flat fiber optic cable are disclosed. The assembly includes a wedge-shaped outer shell with a bottom wall having a friction inner surface with a longitudinal central recess formed therein. The flat fiber optic cable resides within the interior of the outer shell and is supported by the friction inner surface. A shim having two parallel rows of protrusions fits within the interior of the outer shell with the protrusions being in contact with the fiber optic cable. The assembly includes a wedge insert having two outer ridges that substantially align with the two rows of protrusions. When the wedge insert matingly engages the outer shell, the outer ridges press down on the protrusions, which in turn press down on the fiber optic cable mainly at the locations where longitudinal dielectric strength members reside.