Precision in proportional operation of pinch valves along an application-specific path of opening and/or of closing is provided in proportionally controlled pinch valves, systems and methods. Included is the advantageous feature that pinch valves and pinch valve controlling systems and methods can be enhanced by carefully controlling not only two primary operational positions—either fully open or fully closed—but also in-between positions as are required for an application of a user of the pinch valve. The effect on the fluid flowing through tubing that is engaged by the pinch valve head between fully open and fully closed is considered, determined and used to achieve pinch valve operation that is linear in flow change and/or linear in pressure change along the closing path and/or opening path through the tubing. The pinch valves can include a normally closed port that opens when the system experiences a shut-down condition.