Metamaterials are artificial materials with subwavelength structure1 that enable the translation of magnetic2 and electric responses3 into spectral regions not accessible through naturally occurring materials. Here, we report direct measurements of the propagation and confinement of terahertz electromagnetic surface modes tightly bound to flat plasmonic metamaterials that consist of metal surfaces decorated with two-dimensional arrays of subwavelength-periodicity pits. These modes are surface plasmon polaritons with an effective plasma frequency controlled entirely by the surface geometry4. The mode spectrum and penetration depth into air demonstrate strong wavelength-scale energy confinement to the surface below the electromagnetic band edge; this is in stark contrast to the very weak confinement found at flat metal surfaces in this spectral regime. The results are in good agreement with analytical and numerical models of surface plasmon polaritons propagating on structured perfect-conductor surfaces, and imply that plasmonic metamaterials could help miniaturize optical components or lead to improved chemical or biochemical sensors.