Guiding waves through a stable physical channel is essential for reliable information transport. However, energy transport in high-frequency mechanical systems, such as in signal-processing applications1, is particularly sensitive to defects and sharp turns because of back-scattering and losses2. Topological phenomena in condensed matter systems have shown immunity to defects and unidirectional energy propagation3. Topological mechanical metamaterials translate these properties into classical systems for efficient phononic energy transport. Acoustic and mechanical topological metamaterials have so far been realized only in large-scale systems, such as arrays of pendulums4, gyroscopic lattices5,6, structured plates7,8 and arrays of rods, cans and other structures acting as acoustic scatterers9-12. To fulfil their potential in device applications, mechanical topological systems need to be scaled to the on-chip level for high-frequency transport13-15. Here we report the experimental realization of topological nanoelectromechanical metamaterials, consisting of two-dimensional arrays of free-standing silicon nitride nanomembranes that operate at high frequencies (10-20 megahertz). We experimentally demonstrate the presence of edge states, and characterize their localization and Dirac-cone-like frequency dispersion. Our topological waveguides are also robust to waveguide distortions and pseudospin-dependent transport. The on-chip integrated acoustic components realized here could be used in unidirectional waveguides and compact delay lines for high-frequency signal-processing applications.