The response of an electromagnetic flowmeter to the flow rate through it should ideally be independent of the velocity distribution of the liquid within it. In general such flowmeters do not exhibit this ideal behaviour and the variation in response with different velocity distributions, for a given flow rate, can be very large. The sensitivity of a flowmeter to velocity distribution is here described in terms of a ‘worst flow’, which is a particular velocity distribution peculiar to a given flowmeter. The ‘worst flow’ is described mathematically in terms of functions which depend upon the design parameters of the flowmeter. The flowmeter response to its ‘worst flow’, for a given kinetic energy of motion, is formulated. This enables a criterion (ε) to be defined which describes the sensitivity of a given flowmeter to velocity profile effects and which permits different flowmeters to be compared in this respect. Methods of evaluating ε are discussed and its value is calculated for a conventional flowmeter, which employs small electrodes and an approximately uniform magnetic field. It is shown that it is possible actually to generate this worst flow in a given flowmeter, by operating the flowmeter in the role of an electromagnetic pump. This could lead to the direct measurement of ε The possibility is discussed of other definitions of ε based on different boundary conditions and constraints and which might lead to a less severe criterion.