A method for monitoring a state of a sensor installed in a measuring point for detecting the density and/or the mass flow of a medium with at least one oscillator which has been made to vibrate, said oscillator having at least one measuring tube for conducting the medium, wherein a state parameter which characterizes the state depends on at least one other physical parameter of the medium being conducted in the measuring tube, or of the oscillator; wherein the method comprises: Determining tuples which contain a value of the at least one physical parameter and an associated value of the state parameter; assigning each tuple to a range of values of the at least one physical parameter; and forming a reference value (Zi,i) of the state parameter for this range of values of the at least one physical parameter, using the value of the state parameter of the tuple, if a valid reference value of the state parameter is not yet available for this range of values; or comparing the value of the state parameter of the tuple with the reference value, if a reference value of the state parameter is available for this range of values; and generating findings based on the result of the comparison, wherein the state parameter depends on at least three physical parameters of the medium conducted in the measuring tube, in particular on the temperature, density, and pressure of the medium; wherein each determined tuple comprises current values of at least two of the physical parameters and an associated value of the state parameter; wherein the tuples are assigned to a field in a value range matrix of the at least two of the physical parameters, in particular density and temperature; wherein the reference value of the state parameter is formed for this field of the value range matrix, if no valid reference value of the state parameter is available for this field; wherein the value of the state parameter of the tuple is compared with the reference value, if a reference value of the state parameter is available for this field; wherein a ratio of a vibration amplitude of the oscillator to an exciter signal for initiating oscillator vibrations at at least one monitoring frequency is taken into consideration when determining the state parameter, wherein the ratio between the monitoring frequency and a current resonant frequency of the oscillator, in particular the resonant frequency of a bending vibration useful mode, is given by a constant factor. Determining tuples which contain a value of the at least one physical parameter and an associated value of the state parameter; assigning each tuple to a range of values of the at least one physical parameter; and forming a reference value (Zi,i) of the state parameter for this range of values of the at least one physical parameter, using the value of the state parameter of the tuple, if a valid reference value of the state parameter is not yet available for this range of values; or comparing the value of the state parameter of the tuple with the reference value, if a reference value of the state parameter is available for this range of values; and generating findings based on the result of the comparison, wherein the state parameter depends on at least three physical parameters of the medium conducted in the measuring tube, in particular on the temperature, density, and pressure of the medium; wherein each determined tuple comprises current values of at least two of the physical parameters and an associated value of the state parameter; wherein the tuples are assigned to a field in a value range matrix of the at least two of the physical parameters, in particular density and temperature; wherein the reference value of the state parameter is formed for this field of the value range matrix, if no valid reference value of the state parameter is available for this field; wherein the value of the state parameter of the tuple is compared with the reference value, if a reference value of the state parameter is available for this field; wherein a ratio of a vibration amplitude of the oscillator to an exciter signal for initiating oscillator vibrations at at least one monitoring frequency is taken into consideration when determining the state parameter, wherein the ratio between the monitoring frequency and a current resonant frequency of the oscillator, in particular the resonant frequency of a bending vibration useful mode, is given by a constant factor.