Local extrema in the equilibrium magnetic field strength can occur in tokamak plasmas when the plasma beta is increased. Furthermore, the magnetic field strength experienced by an electromagnetic wave propagating along a vertical chord in lower-beta tokamak plasmas may also pass through an extremum. For both these reasons, it is of interest to calculate the absorption of electron cyclotron waves in configurations where a harmonic of the cyclotron resonance lies near an extremum of the equilibrium magnetic field strength. It is shown that strong absorption can occur for both the 0 mode at second harmonic resonance and the X mode at third harmonic resonance, whereas absorption at these resonances is relatively weak when the gradient in magnetic field strength is linear. The optical depth in a magnetic field with parabolic scale length L is typically enhanced with respect to that in a field with linear scale length R by a factor cL/5vTR, where vT is the electron thermal velocity and c the velocity oflight. Since electron cyclotron waves can reach these resonances in high-density plasma from launch positions on the low-field side of the tokamak, the number of effective and convenient electron cyclotron heating configurations is increased when the equilibrium magnetic field strength has local extrema.