The properties of planar, single-layer metamaterials, or metafilms, are studied by varying the structural components of the split-ring resonators used to comprise the overall medium. Measurements and simulations reveal how minor design variations in split-ring resonator structures can result in significant changes in the macroscopic properties of the metafilm. A transmission-line/circuit model is also used to clarify some of the behavior and design limitations of the metafilms. Though our results are illustrated in the terahertz frequency range, the work has broader implications, particularly with respect to filtering, modulation, and switching devices.