A carbon nanotube contact structure can be used for making pressure connections to a DUT. The contact structure can be formed using a carbon nanotube film or with carbon nanotubes in solution. The carbon nanotube film can be grown in a trench in a sacrificial substrate in which a contact structure such as a beam or contact element is then formed by metal plating. The film can also be formed on a contact element and have metal posts dispersed therein to provide rigidity and elasticity. Contact structures or portions thereof can also be plated with a solution containing carbon nanotubes. The resulting contact structure can be tough, and can provide good electrical conductivity.