Non-invasive systems for and methods of determining fluid characteristics within a fluid vessel are disclosed. The methods can include providing a sensor system comprising a single coil magnetic induction conductivity sensor, a processor, and a computing system configured to run an analytical coil-loss model. The method can include calibrating the sensor system to the vessel to provide a column calibration factor. The column calibration factor is dependent upon a cross-sectional area of the vessel and a wall thickness of the vessel. The single coil magnetic induction conductivity sensor can be placed near an external surface of the vessel at a portion of the vessel that is non-conductive. The method can include generating a coil loss measurement utilizing the single coil magnetic induction conductivity sensor and converting the coil loss measurement to a conductivity value of the fluid within the vessel.