In this paper, a new family of pentagonal waveguides is proposed for high‐power microwave transmission. Conformal mapping combined with the finite‐difference method (CMFD) is used to analyze the propagation characteristics of the waveguides. The computed results agree well with the measurements. Finally, compared with other popular numerical methods, some distinguishing advantages of the CMFD are concluded. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 22: 420–423, 1999