The formation of carbon nanotube and superconductor composites makes it possible to produce new and/or improved functionalities that the individual material does not possess. Here we show that coating carbon nanotube forests with superconducting niobium carbide (NbC) does not destroy the microstructure of the nanotubes. NbC also shows much improved superconducting properties such as a higher irreversibility and upper critical field. An upper critical field value of ~5 T at 4.2 K is much greater than the 1.7 T reported in the literature for pure bulk NbC. Furthermore, the aligned carbon nanotubes induce anisotropy in the upper critical field, with a higher upper critical field occurring when the magnetic field is parallel to the carbon nanotube growth direction. These results suggest that highly oriented carbon nanotubes embedded in superconducting NbC matrix can function as defects and effectively enhance the superconducting properties of the NbC.