The remarkable performance of carbon membranes for the selective passage of various species has led to extensive research in designing smart membranes. The mechanical stability of graphene in conjunction with the excellent host-guest chemistry of crown ethers makes the recently synthesized family of crown ether-embedded graphene nanomeshes promising candidates for sieving applications. Inspired by the excellent control over pore architectures offered by such nanomeshes, we investigate the abilities of crown ether-embedded graphene nanomeshes for noble gas separation by the size-sieving mechanism and for He isotope separation by the quantum sieving mechanism. Unlike the previous studies that employ either a finite-difference approach or a wave packet approach, we employ an analytical Eckart potential approach to calculate the tunneling probabilities. Using tunneling-corrected transition-state theory, we examine the competing nature of the zero-point energy effects and tunneling effects in governing the total quantum transmission of the isotopes. Our analysis of the permeation barriers, diffusion rates, transmission probabilities, permeabilities, and selectivities suggests that crown ether-embedded graphene nanomeshes are a class of promising carbon membranes for He isotope separation.