The Weibull modulus and reference strength of ceramic fibers can be inferred from measurements of the tensile stress-strain response of a bundle of such fibers. The goal of the present article is to address issues in the fidelity of results stemming from fiber bundle tests and strategies to optimize outcomes. The issues are addressed through established theorems in uncertainty propagation, Monte Carlo simulations of fiber bundle fracture, and experimental measurements on bundles of SiC fibers of various length and surface condition. The study shows that optimal results are obtained when: (i) tests are performed on fiber bundles with a gauge length that exceeds a critical value (specifically, that needed to prevent mechanical instabilities in the post-load-maximum domain); (ii) bundles are lubricated with a low-viscosity oil, to mitigate both inter-fiber friction and dynamic coupling associated with release waves following fiber fracture; and (iii) the Weibull parameters are obtained by directly fitting the measured stress-strain curves with the function predicted by fiber bundle theory, rather than using methods based on either linear regression analysis of Weibull probability plots or fitting of the peak stress and strain alone.