The goal of the investigations is to estimate the uncertainty in the location of two-dimensional, steady state catchments of pumping wells due to the uncertainty of the spatially variable transmissivity field. The uncertainty is evaluated conditional to measured transmissivity and head data. The uncertainty bandwidth of the catchment boundary is approximated in first order by formulating the conditional transversal second moment of the particle displacements along the expected mean particle trajectory. However, empirical relationships have to be provided for the estimation of the uncertainty in the location of stagnation points. Applications of the approach are presented for a synthetic test case with two arrangements of measurement stations. The results are compared with those from conditional numerical Monte Carlo simulations. The comparison allows an assessment of the accuracy and the applicability of the method. The approximation corresponds quite well with the Monte Carlo simulations.