In order to fabricate nanoscale mechanical devices from high-quality 6H-SiC wafers, a tilted ECR etching technique has been developed that eliminates the need for a buried sacrificial layer. The method applies an anisotropic ECR etch from three different angles relative to the wafer surface in order to pattern and release free-standing structures. Suspended nano-scale, doubly clamped beam resonators have been made as an initial demonstration of this new fabrication method. These beams are the first such structures to be surface nanomachined from 6H-SiC wafers. The availability of 3-dimensional suspended nanostructures from 6H-SiC has opened up the possibility to integrate microwave-frequency nanomechanical devices with SiC-based electronics, and thus significantly broaden the application scope of SiC nanoelectromechanical systems.