At micro- and nanoscales, materials with high Young's moduli and low densities are of great interest for high-frequency micromechanical resonator devices(1-8). Incorporating carbon nanotubes (CNTs), with their unmatched properties, has added functionality to many man-made composites(9-11). We report on the fabrication of <= 100-nm-thick laminates by sputter-deposition of aluminium onto a two-dimensional single-walled CNT network(12,13). These nanolaminates - composed of Al, its native oxide Al(2)O(3) and CNTs - are fashioned, in a scalable manner, into suspended doubly clamped micromechanical beams. Dynamic flexural measurements show marked increases in resonant frequencies for nanolaminates with Al - CNT laminae. Such increases, further supported by quasi- static flexural measurements, are partly attributable to enhancements in elastic properties arising from the addition of CNTs. As a consequence, these nanolaminate micromechanical resonators show significant suppression of mechanical nonlinearity and enhanced strength, both of which are advantageous for practical applications and analogous to biological nanocomposites, similarly composed of high-aspect-ratio, mechanically superior mineral platelets in a soft protein matrix(14).