Design of microwave devices based on a combination of traditional right-handed transmission line sections with positive dispersion and metamaterial lefthanded transmission line sections with negative dispersion is considered. Compared to homogeneous transmission lines, the use of cascaded line sections gives additional degrees of freedom for the design of microwave devices with enlarged functionality and unique performance. Artificial right-and left-handed transmission lines based on lumped-element equivalent cells help to minimize the dimensions of microwave devices. For filters, a combination of cascaded right-and left-handed transmission lines can be applied advantageously, to control the position and the widths of the individual pass-bands and the parasitic response of higher harmonics. This paper describes the theoretical approach to the design of multi-band resonators and filters with highly suppressed response of higher harmonics. Selected devices were manufactured as three-dimensional ceramic multilayer modules based on low-temperature co-fired ceramic technology. The results of numerical simulation and experimental investigation of these devices are compared. Furthermore, the employment of variable capacitors in single cells of artificial transmission lines provides frequency tuning of the devices. The design of tunable dual-band filters is discussed, and the experimental results are presented.