Objects produced by conventional three-dimensional printing methods often have limited structural quality. Printing compositions to address this issue can include a solidifiable matrix and a plurality of carbon nanostructures dispersed in the solidifiable matrix. The carbon nanostructures include a plurality of carbon nanotubes that are branched, crosslinked, and share common walls with one another. Three-dimensional printing methods utilizing such printing compositions can include: depositing the printing composition in a layer-by-layer deposition process, and while depositing the printing composition, applying a focused input of microwave radiation in proximity to a location where the printing composition is being deposited. The focused input of microwave radiation heats the carbon nanostructures at the location and promotes consolidation of the printing composition within an object being produced by the layer-by-layer deposition process.