The copper-stabilizer continuity measurement - or CSCM - was devised to obtain a direct and complete qualification of the continuity in the 13 kA bypass circuits of the LHC, especially in the copper-stabilizer of the busbar joints and the bolted connections in the diode-leads. The circuit under test is brought to ~20 K, a voltage is applied to open the diodes, and the low-inductance circuit is powered with a pre-defined series of current profiles. The profiles are designed to successively increase the thermal load on the busbar joints up to a level that corresponds to worst-case operating conditions at nominal energy. In this way, the circuit is tested for thermal runaways in the joints - the very process that could prove catastrophic if it occurred under nominal conditions with the full circuit energy. Surveillance software and a numerical model were devised to carry out the analysis and ensure complete protection of the circuit from over-heating. A type test of the CSCM was successfully carried out in April 2013 on one main dipole and one main quadrupole circuit of the LHC. This paper describes the analysis procedure, the numerical model, and results of this first type test.