In this study, transmission characteristics of split-ring resonator (SRR) and double-sided SRR (DSRR) are investigated using Ansoft's HFSS software, for varying values of substrate parameters, which are thickness, the real part of relative permittivity and the dielectric loss tangent of the substrate. Simulation results have shown that resonance patterns of both SRR and DSRR are affected similarly from permittivity and loss tangent variations. However, changes in the substrate thickness affect their resonance characteristics quite differently. Resonance frequency, resonance strength, and bandwidth of the resonance curve noticeably decrease for the DSRR structure in response to decreasing substrate thickness while the resonance frequency of, the SRR increases at a comparatively slower rate without any noticeable change in the bandwidth and the resonance strength. Besides, the simulation results show that doubling the SRR (i.e., using DSRR), while keeping the unit cell dimensions fixed, provides an electrically smaller structure, and thus better effective medium approach.