Organic second-order nonlinear optical (NLO) materials have been shown to offer faster NLO response times and higher bandwidths in electro-optic (EO) devices than their inorganic counterparts, such as lithium niobate. In practice, the second-order NLO response is measured in the bulk in EO devices, or using techniques such as hyper-Rayleigh Scattering (HRS). However, the design of improved NLO molecules requires understanding of the NLO response on the single-molecule level. In this study, we use modern computational approaches such as density functional theory (DFT) and high-level electron correlation (post-Hartree-Fock) methods to understand the intrinsic NLO character of the individual molecules of these materials. Particularly, we focus on the long-range correction (LC) and range-separated hybrid (RSH) DFT methods. In this work, we utilize a 14-molecule benchmarking set of well-characterized NLO chromophores and compare calculated results with the corresponding experimentally measured linear and nonlinear optical properties, respectively, the peak one-photon absorption energy, λmax, and first-order hyperpolarizability, β. We particularly focus on determining the amount of exact exchange (ω, the range-separation parameter) in LC/RSH-DFT methods for accurately computing these properties for this class of chromophores. In addition, second-order Møller-Plesset perturbation (MP2) is used to explore the effectiveness of a post-Hartree-Fock method in contrast with DFT.