Method for monitoring a flow rate of a medium, which has at least one liquid phase, by means of a Coriolis mass flow meter, and a differential pressure meter which is set up to determine a pressure difference between a first pressure measuring point and a second pressure measuring point on a pipeline, wherein the Coriolis mass flow meter is arranged between the first pressure measuring point and the second pressure measuring point in the pipeline, wherein the Coriolis mass flow meter serves as a differential pressure transmitter, wherein the first pressure measuring point is arranged between a pressure source and the Coriolis mass flow meter, wherein the second pressure measuring point is arranged between the Coriolis mass flow meter and a pressure sink; wherein the Coriolis mass flow meter has at least two oscillators each with at least one bent measuring tube, wherein the bent measuring tubes each have a vertex which is arranged at the lowest point of the measuring tube in relation to a local gravitational field, wherein the measuring tubes of the oscillators are arranged between two collectors, through which the measuring tubes are connected in parallel in terms of flow, wherein a first vertex of a measuring tube of a first oscillator is arranged above a second vertex of a measuring tube of a second oscillator, wherein the method comprises the following steps: Detection of a pressure difference between the first pressure measuring point and the second pressure measuring point; Detecting a first density measurement value based on at least a first oscillation frequency of the first oscillator; detecting a second density measurement value based on at least a second oscillation frequency of the second oscillator; Determining a flow measurement value based on the pressure difference when a difference between the first density measurement value and the second density measurement value is less than a density difference limit value. wherein the Coriolis mass flow meter has at least two oscillators each with at least one bent measuring tube, wherein the bent measuring tubes each have a vertex which is arranged at the lowest point of the measuring tube in relation to a local gravitational field, wherein the measuring tubes of the oscillators are arranged between two collectors, through which the measuring tubes are connected in parallel in terms of flow, wherein a first vertex of a measuring tube of a first oscillator is arranged above a second vertex of a measuring tube of a second oscillator, wherein the method comprises the following steps: Detection of a pressure difference between the first pressure measuring point and the second pressure measuring point; Detecting a first density measurement value based on at least a first oscillation frequency of the first oscillator; detecting a second density measurement value based on at least a second oscillation frequency of the second oscillator; Determining a flow measurement value based on the pressure difference when a difference between the first density measurement value and the second density measurement value is less than a density difference limit value. Detection of a pressure difference between the first pressure measuring point and the second pressure measuring point; Detecting a first density measurement value based on at least a first oscillation frequency of the first oscillator; detecting a second density measurement value based on at least a second oscillation frequency of the second oscillator; Determining a flow measurement value based on the pressure difference when a difference between the first density measurement value and the second density measurement value is less than a density difference limit value.