Over current stabilization of YBa2Cu30x (YBCO) coated conductor high temperature superconductor tape is required in most applications. The conductor must carry currents in excess of the critical current, Ic, without damage during over current events. Conductor damage is the result of joule heating and excessive temperature rise in regions with low Ic. We have developed and applied a measurement technique using a locally applied magnetic field with a high spatial gradient to define a small area over which the Ic is depressed. By measuring the voltage and temperature as a function of current, power dissipation and temperature rise were determined. Unstabilized conductors experienced thermal runaway and are easily damaged. Copper stabilizers applied by electroplating decreased dramatically the temperature rise and increased the level of power dissipation compared with the unstabilized conductor.