We present an electrically-controlled nematic-liquid-crystal-filled double-prism structure that can be used to simulate quantum-mechanical tunneling through a barrier of variable height. Measurements of time delay in reflection from this structure, taken with femtosecond resolution using entangled photon pairs in a Hong-Ou-Mandel interferometer, are compared to theoretical predictions. We show that the Goos-Hanchen contribution to the tunneling delay is unmeasurable in this geometry. Our research contributes to the understanding of quantum-mechanical barrier tunneling times, and can lead to the fabrication of optical analogues to the tunnel junction and other photonic devices.