Surface plasmons (SPs) are interface waves very similar to Zenneck waves but existing only at optical frequencies where metals exhibit a negative permittivity. The availability of novel structured metamaterials with tailorable positive/negative constitutive parameters allows the generation of SPs in the microwave range, which may lead to novel components and antennas applications. This paper describes SPs existing at the interface between a right-bunded (RH) and a left-handed (LH) materials. The dispersion relation is established, the properties of these SPs are discussed, a transmission line (TL) LC implementation of the RH/LH interface is proposed, and the phenomena are demonstrated by full-wave simulation in an effective medium approach.