After a short introduction of the wake potentials and coupling impedances, a few new results in impedance calculations are discussed. The first example is a new analytical method for calculating impedances of axisymmetric structures in the low frequency range, below the cutoff frequency of the vacuum chamber. The second example demonstrates that even very small discontinuities on a smooth waveguide can result in appearance of trapped modes, with frequencies slightly below the waveguide cutoff frequency. The high‐frequency (above the cutoff) behavior of the coupling impedance of many small discontinuities is discussed in the third example. © 1995American Institute of Physics