Carbon nanotubes (CNTs) impart great multi-functionality when reinforced with a polymer matrix. This paper shows the qualitative and quantitative improvements of the mechanical, electrical, and electromagnetic interference shielding effectiveness properties with the additions of the multiwalled carbon nanotubes (MWCNTs) and functionalized MWCNTs (FMWCNTs) in ethylene methyl acrylate (EMA) polymer. Mechanical characterization is performed through tensile testing, and electromagnetic interference shielding effectiveness (EMI SE) is calculated from the scattering parameters obtained from the vector network analyzer. Both properties improve compared to neat polymer with the reinforcement loadings up to a critical value, from where the properties start to degrade due to the agglomeration of the CNTs. FMWCNTs provide better performance in terms of properties over the MWCNT reinforced nanocomposites. Morphological characterization using a scanning electron microscope justifies a lower percolation threshold of FMWCNT/EMA composite by better electrical conductive network formation. At 10 wt% of FMWCNT loading, the FMWCNT/EMA composite shows 25.1 dB of EMI shielding efficiency combined with excellent mechanical and electrical properties extending its potential use in both industry and academia as an excellent flexible EMI shielding material.