Coated conductors are promising material for the construction of high field magnets, but the slow propagation velocity of the normal zone makes the protection against quenches a critical issue. The quench protection system for a small insert coil under development at CRPP has been studied. The voltage drop and the hot spot temperature during the quench have been estimated using analytical expressions; the cross section of the copper stabilizer, the voltage threshold and the time constant were set as parameters. Detailed calculations have been carried out using the Cryosoft code THEA. The copper cross section available from the tape manufacturer is enough to ensure that the hot spot temperature remains below 200 K, but only in conjunction with a sensitive quench detection system (voltage threshold lower than 100 mV) and a fast dumping time (time constant shorter than 100 ms). These requirements can be fulfilled in the small insert coil under construction, because the inductance is about 50 mH and because the coil can be quickly discharged independently from the main magnet. The passive protection circuit consists of dump resistor and diodes. In case of longer time constants (few seconds), a larger copper cross section (comparable to the one used in low temperature superconducting magnets) is required in order to maintain the temperature within safe values.