Due to the unique combination of physicochemical and structural properties of carbyne-enriched nanocoatings, they can be used for the development of high-end electronic devices. We propose using it for the development of sensor platforms based on silicon bulk micromachined membranes that serve as a part of microcapacitors with flexible electrodes, with various sizes and topologies. The carbyne-enriched nanocoating was grown using the ion-assisted pulse-plasma deposition method in the form of 2D-ordered linear-chain carbon with interchain spacing in the range of approximately 4.8–5.03 Å. The main characteristics of the fabricated sensors, such as dynamic range, sensitivity, linearity, response, and recovery times, were measured as a function of the ethanol concentration and compared for the different sizes of the micromembranes and for the different surface states, such as patterned and non-patterned. The obtained results are the first step in the further optimization of these sensor platforms to reach more precise detection of volatile organic compounds for the needs of the healthcare, air monitoring, and other relevant fields of human health.