Recent experiments have revealed two distinct percolation phenomena in carbon nanotube (CNT)/polymer nanocomposites: one is associated with the electrical conductivity and the other is with the electromagnetic interference (EMI) shielding. At present, however, no theories seem to exist that can simultaneously predict their percolation thresholds and the associated conductivity and EMI curves. In this work, we present an effective-medium theory with electrical and magnetic interface effects to calculate the overall conductivity of a generally agglomerated nanocomposite and invoke a solution to Maxwell’s equations to calculate the EMI shielding effectiveness. In this process, two complex quantities, the complex electrical conductivity and complex magnetic permeability, are adopted as the homogenization parameters, and a two-scale model with CNT-rich and CNT-poor regions is utilized to depict the progressive formation of CNT agglomeration. We demonstrated that there is indeed a clear existence of two separate percolative behaviors and showed that, consistent with the experimental data of poly-L-lactic acid (PLLA)/multi-walled carbon nanotube (MWCNT) nanocomposites, the electrical percolation threshold is lower than the EMI shielding percolation threshold. The predicted conductivity and EMI shielding curves are also in close agreement with experimental data. We further disclosed that the percolative behavior of EMI shielding in the overall CNT/polymer nanocomposite can be illustrated by the establishment of connective filler networks in the CNT-poor region. It is believed that the present research can provide directions for the design of CNT/polymer nanocomposites in the EMI shielding components.