We have built coils with MnZn ferrite cores that demonstrate an appreciable giant magnetoelectric effect (GME). Their maximum magnetoelectric (ME) output is as high as 87 V/Oe at tens of kilohertz, which is remarkable for devices without any power supply. Our experimental and theoretical analyses suggest that the GME of the coils originates from LC resonances. Our results show a practical way to design ME devices such as passive high-frequency sensitive magnetic sensors. We have found as well that attention should be paid to LC resonance when performing ME spectral measurements.