A novel solution to the estimation of catchment rainfall at a sub-hourly resolution from measured streamflow is introduced and evaluated for two basins with markedly different flow pathways and rainfall regimes. It combines a continuous-time transfer function model with regularised derivative estimates obtained using a recursive method with capacity for handling missing data. The method has general implications for off-line estimation of unknown inputs as well as robust estimation of derivatives. It is compared with an existing approach using a range of model metrics, including residuals analysis and visuals; and is shown to recover the salient features of the observed, sub-hourly rainfall, sufficient to produce a precise estimate of streamflow, indistinguishable from the output of the catchment model in response to the observed rainfall data. Results indicate potential for use of this method in environment-related applications for periods lacking sub-hourly rainfall observations.