Using the transmission-line theory, we investigate properties of wave propagation and resonance in a pre-Cantor multilayer called pre-Cantor bars whose interval is [0,L]. When the stage number n increases, the pre-Cantor bar will not transmit almost anywhere for [variant_greek_epsilon]r2 > 1 where [variant_greek_epsilon]r2 is the ratio of dielectric constants of two kinds of layers. For resonance frequencies of the n-th pre-Cantor bar, the largest amplitude of voltage at the midpoint of the bar, V(L2), increases double-exponentially because of the inequality |V(L2)|≤[variant_greek_epsilon]r22n-2. For such a resonance frequency, the amplitude of the voltage at the midpoint of an interval [L3k+1,2L3k+1] is given by |V(L2·3k)|≤[variant_greek_epsilon]r22n-k-2 where k = 1,2, ..., n - 1. Because the voltage |V(x)| is localized around x = L2, the electro-magnetic wave (EM) localization occurs for the resonance frequencies of the pre-Cantor bar of the higher stages. Using a microstripline of the 3rd stage Cantor structure we will show that the measured transmission spectrum is consistent with the ideal one if the dissipation factor of the substrate is tan δ = 0.023 that is a typical value for the substrate of glassy epoxy resin in microwave frequencies. [ABSTRACT FROM AUTHOR]