Acid modified multiwalled carbon nanotubes (a-MWCNT) reinforced polyurethane (PU) composite films have been fabricated using a solvent casting technique with 0-10 wt% of a-MWCNTs. A nanoindentation study has been carried out on these films in order to investigate the mechanical properties. Incorporation of a-MWCNTs in a PU matrix led to a drastic increase in the hardness and elastic modulus. The maximum nanoindentation hardness of 217.5 MPa for 10 wt% a-MWCNT loading was observed as compared to 58.5 MPa for pure PU (an overall improvement of 271%). The nanoindentation elastic modulus for a 10 wt% a-MWCNT loaded sample was 1504.2 MPa as compared to 385.7 MPa for pure PU (an overall improvement of 290%). In addition to hardness and elastic modulus, other mechanical properties i.e. plastic index parameter, elastic recovery, ratio of residual displacement after load removal and displacement at the maximum load and plastic deformation energy have also been investigated. The enhancement in the mechanical properties was correlated with spectroscopic and microscopic investigations using Raman spectroscopy, SEM and TEM. Dispersion of a-MWCNTs in the PU matrix was studied using Raman mapping. Besides the improvement in mechanical properties, the electromagnetic interference shielding properties were also investigated in the 8.2-12.4 GHz (X-band) frequency range. A value of $29 dB for the 10 wt% MWCNT loaded sample having a thickness of 1.5 mm was obtained.Therefore, these polyurethane composite films shall not only be useful for hard and scratchless coatings but also for protection from electromagnetic radiation in making electromagnetic shielding bags for packaging of electronic circuits and for scratchless tape for laminating circuit boards.