A large proportion of the recent growth of the volume of electromagnetics research has been associated with the emergence of so called electromagnetic metamaterials1 and the discovered ability to design their unusual properties by tweaking the geometry and structure of the constituent “meta-atoms”. For example, negative permittivity and negative permeability can be achieved, leading to negative refractive index metamaterials. The negative permeability could be obtained via geometrical control of high frequency currents, e.g. in arrays of split ring resonators, or alternatively one could rely on spin resonances in natural magnetic materials, as was suggested by Veselago. The age of nanotechnology therefore sets an intriguing quest for additional benefits to be gained by structuring natural magnetic materials into so called magnonic metamaterials, in which the frequency and strength of resonances based on spin waves (magnons) are determined by the geometry and magnetization configuration of meta-atoms. Spin waves can have frequencies of up to hundreds of GHz (in the exchange dominated regime) and have already been shown to play an important role in the high frequency magnetic response of composites. Moreover, in view of the rapid advances in the field of magnonics, which in particular promises devices employing propagating spin waves, the appropriate design of magnonic metamaterials with properties defined with respect to propagating spin waves rather than electromagnetic waves acquires an independent and significant importance.