Metamaterial structures and devices based on them are now widely used in military and civilian communications and radar equipment. Practically most of them are built on the basis of flat microstrip structures based on the so-called split ring resonators (SRR). Two types of microwave structures based on resonators that are not interconnected and connected in parallel to each other directly between the inputs and outputs of microwave devices are considered. Structures using stripline resonators of different lengths (different sizes), as well as dielectric ones excited by different types of oscillations, have been studied. They are modeled both using dipole representations and on the basis of even and odd (in-phase and anti-phase) types of oscillations. An analogy of this kind of structures with SRR is demonstrated, the appearance of which has intensified the study of the properties of metamaterials and their practical applications. Structures using a single mode of vibration excited by orthogonal circular modes of polarization (left-handed and right-handed circular polarization), also known in the literature as “chiral” modes, are modeled on the basis of normal modes of vibration (left-handed and right-handed polarized). As one of the results of this article, it demonstrates that both of these approaches can be reduced to both modeling using normal oscillations and modeling using balanced x-networks. The duality of the parameters of the scattering matrices of bandpass and band-stop filters is also illustrated.