ABSTRACT Assessing the likelihood that the rotation curve of a galaxy matches predictions from galaxy formation simulations requires that the uncertainties in the circular speed as a function of radius derived from the observational data be statistically robust. Few uncertainties presented in the literature meet this requirement. In this paper, we present a new standalone tool, makemap, that estimates the fitted velocity at each pixel from Gauss–Hermite fits to a 3D spectral data cube, together with its uncertainty obtained from a modified bootstrap procedure. We apply this new tool to neutral hydrogen spectra for 18 galaxies from the THINGS sample, and present new velocity maps with uncertainties. We propagate the estimated uncertainties in the velocity map into our previously described model fitting tool DiskFit to derive new rotation curves. The uncertainties we obtain from these fits take into account not only the observational errors, but also uncertainties in the fitted systemic velocity, position of the rotation centre, inclination of the galaxy to the line of sight, and forced non-circular motion. They are therefore much better-defined than values that have previously been available. Our estimated uncertainties on the circular speeds differ from previous estimates by factors ranging up to of five, being smaller in some cases and larger in others. We conclude that kinematic models of well-resolved H i data sets vary widely in their precision and reliability, and therefore potentially in their value for comparisons with predictions from cosmological galaxy formation simulations.