The electrical tuning of negative dielectric anisotropy (−Δε) cholesteric liquid crystals (CLCs) under the influence of ac and dc electric fields was studied. Unlike (+Δε) CLCs, these materials align their helical axis along the applied electric field, allowing the preservation of the optical band gap. Our results show band gap shifts greater than 20% of the original notch position with little change in the quality of the band gap, including the bandwidth and notch depth. These results can be understood by using an electromechanical model, which shows that the Maxwell’s stresses are sufficiently strong to distort the ITO glass substrates. Simple beam and plate elasticity theory is shown to adequately describe the observed behavior. The electromechanical effect is then used to create CLC cells, which can both red and blue tune. This mechanism may have interesting applications in tunable optical filters, optical pressure/stress sensors, and tunable laser technologies.