A system for measuring the flow properties of a tear duct, to ascertain its flow resistance, includes a syringe communicating with a cannula to supply liquid to a punctum of an eye, the cannula having a tip to seal to the punctum. A motor is arranged to actuate the syringe. A pressure sensor monitors the pressure of the liquid supplied to the punctum. A monitoring circuit provides an indication of the flow resistance. A feedback circuit controls the motor in accordance with the measured pressure, to maintain a preset liquid pressure, or to ensure that the liquid pressure does not exceed a preset threshold. The system may prevent flow through the other punctum of the eye. If the flow rate of the liquid supplied to the punctum is also monitored, the monitoring circuit is arranged to determine the flow resistance from the pressure and the flow rate.