Absorption of ion Bernstein (IB) waves by electrons is investigated. These waves are excited by linear mode conversion in tokamak plasmas during fast wave (FW) heating andcurrent drive experiments in the ion cyclotron range of frequencies.Near mode conversion, electromagnetic corrections to the local dispersionrelation largely suppress electron Landau damping of these waves, whichbecomes important again, however, when their wavelength is comparable tothe ion Larmor radius or shorter. The small Larmor radius wave equationssolved by most numerical codes do not correctly describe the onset ofelectron Landau damping at very short wavelengths, and these codes,therefore, predict very little damping of IB waves, incontrast to what one would expect from the local dispersion relation.We present a heuristic, but quantitatively accurate, model which allows account tobe taken of electron Landau damping of IB waves in suchcodes, without affecting the damping of the compressional wave or the efficiencyof mode conversion. The possibilities and limitations of this approach arediscussed on the basis of a few examples, obtained by implementing thismodel in the toroidal axisymmetric full wave code TORIC.