We present Top-kriging, or topological kriging, as a method for estimating streamflow-related variables in ungauged catchments. It takes both the area and the nested nature of catchments into account. The main appeal of the method is that it is a best linear unbiased estimator (BLUE) adapted for the case of stream networks without any additional assumptions. The concept is built on the work of Sauquet et al. (2000) and extends it in a number of ways. We test the method for the case of the specific 100-year flood for two Austrian regions. The method provides more plausible and, indeed, more accurate estimates than Ordinary Kriging. For the variable of interest, Top-kriging also provides estimates of the uncertainty. On the main stream the estimated uncertainties are smallest and they gradually increase as one moves towards the headwaters. The method as presented here is able to exploit the information contained in short records by accounting for the uncertainty of each gauge. We suggest that Top-kriging can be used for spatially interpolating a range of streamflow-related variables including mean annual discharge, flood characteristics, low flow characteristics, concentrations, turbidity and stream temperature.