Fusion power production is the ultimate goal of fusion research, and its determination is crucial in any fusion energy application. In this paper the principles of collimated neutron flux measurements for fusion plasma power determination are described. In this method, a high-resolution neutron spectrometer provides an absolutely calibrated neutron flux, and a neutron profile monitor ("camera") gives information on the neutron emission profile of the plasma. The total neutron flux seen by the spectrometer is discussed in terms of direct and scattered flux, and a model is set up to evaluate the magnitude of these different components. Particular care is taken to estimate the uncertainties involved, both in the model and the measurements. The method is put to practical use at JET, where a magnetic proton recoil spectrometer and a neutron profile monitor are available. Results from JET's trace tritium experimental campaign in 2003 are presented and show that the systematic uncertainties in fusion power measurements are reduced in comparison to what has been presented for foil activation systems. A systematic error of 6% is reported here. For ITER these results imply that the fusion power can be redundantly measured and with better accuracies than for traditional methods.