TLD-300 (CaF2:Tm) dosimeters were used to measure the absorbed dose in an experimental assembly simulating the shield and the superconducting coils of a fusion reactor irradiated by 14-MeV neutrons. The shield was formed by plates of Type 316 stainless steel and by a water-equivalent material (Perspex), while a second block made of Type 316 stainless steel and copper plates simulated the superconducting coils of the tokamak. Since the TLD-300 shows two main peaks, one of which is more sensitive to neutrons, the neutron and gamma doses were separated using the two-peak method. The resulting absorbed neutron dose was 30% of the total in positions close to the neutron source, while its contribution was negligible (< 7%) in the superconducting coils. The total dose level to be studied ranged from a few tens of micrograys to 10 Gy. Because the latter value was expected to be out of the linear response range for the TLD-300, the supralinear effects for the TLD-300 were studied as well as its sensitivity to determine the possibility of its use for doses as low as 10 μGy. Since the detector background can introduce an uncertainty of less than ±10%, the measurement of very low doses was performed with a total error lower than ±15%.