Slit‐grid emittance measurement devices usually do not scan the beam continously but in fixed linear (x) and angular (x’) steps. Thus in an emittance measurement performed with a slit‐grid system, the beam is represented by a number of phase space boxes with a constant area or volume determined by the linear and angular resolution. Considering the emittance as the area in the two‐dimensional subspace (x,x’) covered by the beam, the quantization error and its dependence on the resolution (linear and angular) as well as the influence of the beam parameters is discussed. Measuring the very low emittance of the high efficiency source (HIEFS) proved that the quantization error can be unacceptably high (≫100%). With an optimized measuring device, the normalized emittance came down from 10−1to 3.6×10−3&pgr; mm mrad. Finally, a typical misleading result of an emittance measurement, caused by the quantization error, is presented.