Stable delivery of liquids to microfluidic systems is essential for their reproducible functioning, especially when supplying flows to organs-on-chips – delicate living models that recreate human physiology on the microscale and thus can be used to reduce the need for animal testing. Most flow control systems are unable to sustain a robust and stable flow in longer experiments (>1 week), particularly those based on the ubiquitous syringe pump. Though easy to use, syringe pumps have no mechanism for actually measuring flow, let alone flow regulation with sensor feedback. We have developed a liquid delivery system based on the generation of flow by applying a constant air pressure to liquids in sealed containers. A flow of liquid is monitored by accurate measurement of mass flows (mg/min) using downstream Coriolis-based mass flow sensors. Measured mass flows provide fast feedback to integrated valves, with valves opening or closing slightly to increase or decrease solution flows to the organs-on-chips as required. This mass flow sensing principle is not affected by changes in the density, temperature, and viscosity of the liquids being displaced. This is in contrast to systems that use volumetric flow sensors, which require recalibration when these parameters change. The rationale behind using this principle for organs-on-chips, is that the stability provided by this flow control system allows for more control over growth of these mini-organs. We demonstrate the functionality of this system with three examples: 1) Fast stabilization (within seconds) under changing physical conditions; 2) Short-term stability (minutes to hours) of delivered flows in a microreactor with interconnected inlets; and 3) Long-term stability (>1 week) of cell medium flows to a living organ-on-a-chip. Two categories of organs-on-chips (OOCs) can be distinguished: 1) solid OOC are designed for three-dimensional cell or tissue constructs that interact with each other and their surroundings, and 2) barrier-type OOC contain a selective cellular barrier between two compartments as do many barriers in the body. The latter of these two types is the most challenging to culture and maintain as they are very sensitive to variations in flow and pressure surges. The flow control system presented in this work provides a great improvement compared to the use of syringe pumps and volumetric flow sensors in OOC studies. The novelty of this work lies in the long-term stability use of this system for organs-on-chips, maintaining stability for short to very long periods of time without compromising the barrier function of the organ-on-chip by pressure surges, bacterial contamination, or other undesired effects from the flow delivery system.