We present a new scheme to estimate the elastic properties of biological membranes in computer simulations. The method analyzes the thermal fluctuations in terms of a coupled undulatory mode, which disentangle the mixing of the mesoscopic undulations and the high-q protrusions. This approach makes possible the accurate estimation of the bending modulus both for membranes under stress and in tensionless conditions; it also extends the applicability of the fluctuation analysis to the small membrane areas normally used in atomistic simulations. Also we clarify the difference between the surface tension imposed in simulations through a pressure coupling barostat, and the surface tension that can be extracted from the analysis of the low wave vector dependence of the coupled undulatory fluctuation spectrum. The physical analysis of the peristaltic mode is also refined, by separating the bulk and protrusions contributions. We illustrate the procedure by analyzing 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine bilayers. The bending moduli obtained from our analysis, shows good agreement with available experiments.