Metamaterials (MM) represent a class of artificially-made structures, exhibiting, if properly designed, negative values of effective permittivity and permeability in specific spectral regions simultaneously. Recently, such structures have indeed attracted much attention due to their unique optical behavior not found in nature. These structures offer, e.g. a possibility of practical realization of perfect lenses, possessing a spatial resolution below the wavelength limit. In this contribution, we have focused on theoretical rigorous study on one specific class of MM structures, called fishnets, consisting of a combination of metal and dielectric layers with periodically arranged sub-wavelength holes. Our attempt was to reveal the physics and optimize the fishnet structure by tailoring the geometrical features in order to achieve optimized response in terms of negative refraction indices in particular spectral regions. For that purpose, our in-house 2D rigorous coupled wave analysis (RCWA) software was used for rigorous computing, the results of which were afterwards post-processed in order to retrieve the effective parameters. Using this tool, with the help of our approximate model, enabling more physical insight of wave-coupling processes, numerical simulations of plane-wave excitation of the multilayered nanofishnets have thus been performed. The reflection and transmission coefficients have been calculated and the effective material parameters have consequently been extracted from the obtained data, via the homogenization procedure.