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We present a design and details of construction of two calorimetric systems that allow us to measure the total loss in high temperature superconducting coils or linear samples carrying alternating current while exposed to a strong alternating magnetic field. This measurement technique is based on the boil-off of liquid nitrogen. The first system is designed to measure ac losses in superconducting coils in self-field generated by AC transport current. The second system contains a permanent magnet rotor and simulates the environment of an electric motor or generator. The sensitivity of the system is such that it can measure low losses from a few milliwatts to several hundred milliwatts, in either a static or dynamic magnetic field.