We have succeeded in detecting the degradation of cable’s polymeric insulation well before its continual use becomes risky. Degradation of organic polymers is mainly caused by oxidation if the ambience around the cable contains oxygen. When organic polymers are oxidized, polar carbonyl groups are formed, by which the permittivity is increased. This in turn decreases the characteristic impedance of a polymer-insulated cable. If we inject electromagnetic waves in a very wide frequency range into the cable and measure the ratio of reflected power to injected power, the information on the effects of the characteristic impedance changes is included in the frequency spectra of the ratio. If we do inverse Fourier transform, we can convert the data to a time domain. Therefore, we can know the degraded portion by multiplying the velocity of electromagnetic waves in the cable.