Electrodynamic characteristics and parameters of the double‐gap klystron resonator with the inductive microstrip elements on the suspended ceramic substrate has been investigated. The inductive part of a resonator made on the basis of a quasi‐fractal Sierpinski's triangle, and a capacitor part, made between end faces of the multi‐channel drift tubes and forming a double gridless gap. The developed resonator can find application in micro vacuum klystron devices working in the systems of telecommunication and navigation in 1‐ and multi‐frequency mode of operation.