Sidewall transfer lithography (STL) is demonstrated as a method for parallel fabrication of 2D nanostructured cellular solids in single-crystal silicon. The linear mechanical properties of four lattices (perfect and defected diamond; singly and doubly periodic honeycomb) with low effective Young's moduli and effective Poisson's ratio ranging from positive to negative are modelled using analytic theory and the matrix stiffness method with an emphasis on boundary effects. The lattices are fabricated with a minimum feature size of 100 nm and an aspect ratio of 40:1 using single- and double-level STL and deep reactive ion etching of bonded silicon-on-insulator. Nanoelectromechanical systems (NEMS) containing cellular materials are used to demonstrate stretching, bending and brittle fracture. Predicted edge effects are observed, theoretical values of Poisson's ratio are verified and failure patterns are described.