Coarse-grain multi-threshold CMOS (MTCMOS) is an effective power-gating technique to reduce ICs leakage power consumption by turning off idle devices with MTCMOS power switches. In this paper, we study the usage of coarse-grain MTCMOS power switches for both logic circuits and SRAMs, and then propose corresponding methods of testing stuck-open power switches for each of them. For logic circuits, a specialized ATPG framework is proposed to generate a longest possible robust test while creating as many effective transitions in the switch-centered region as possible. For SRAMs, a novel test algorithm is proposed to exercise the worstcase power consumption and performance when stuck-open power switches exist. The experimental results based on an industrial MTCMOS technology demonstrate the advantage of our proposed testing methods on detecting stuck-open power switches for both logic circuits and SRAMs, when compared to conventional testing methods.