The process of determining the uncertainty in the neutron fluence from the measured activity of a dosimetry monitor is reviewed and the importance of treating the energy-dependent correlation is illustrated using several representative neutron fields. The process of determining the uncertainty in the neutron fluence when a transfer calibration is used is then detailed. The conversion factor, when a transfer calibration is used, has a term that has an integral over the cross section appearing in both the numerator and the denominator. This term introduces a nonlinear dependence on the cross section within the conversion factor and an explicit correlation between the terms appearing in the numerator and denominator of the conversion factor. A method for rigorously treating this nonlinear uncertainty propagation is presented. This method is based upon utilizing the covariance matrix for the cross section and utilizing a statistical sampling approach based on a Cholesky transformation of this covariance matrix. This methodology is then applied to the determination of the uncertainty from a transfer calibration for a set of nine neutron spectra based upon using the 32S(n,p)32P reaction and a transfer calibration in a 252Cf standard benchmark neutron field. A very strong correlation is found in the cross-section terms as they appear in the numerator and in the denominator. When a rigorous treatment is used to propagate the uncertainty due to the cross section for the dosimetry monitor, the uncertainty in the conversion factor is reduced by a factor of more than ten times from a worst-case approach that treats the uncertainty components in the numerator and denominator as uncorrelated. This ten times difference is also seen when the comparison is made between a rigorous treatment and a treatment of the cross-section contributions where the numerator and denominator are treated as uncorrelated (i.e., when compared to a root-mean-square approach).