For the first time, nanoporous Al2O3 templates with smoothed surface relief characterized by flattened interpore areas were used in the fabrication of Co/Pd and Co/Pt multilayers (MLs) with strong perpendicular magnetic anisotropy (PMA). Alternating gradient magnetometry (AGM) revealed perfectly conserved PMA in the Co/Pd and Co/Pt porous MLs (antidot arrays) with a ratio of remanent magnetization (M-r) to saturation magnetization (M-S) of about 0.99, anisotropy fields (H-a) of up to 2.6 kOe, and a small deviation angle of 8 degrees between the easy magnetization axis and the normal to the film surface. The sufficient magnetic hardening of the porous MLs with enhanced coercive field H-C of up to similar to 1.9 kOe for Co/Pd and similar to 1.5 kOe for Co/Pt MLs, as compared to the continuous reference samples (similar to 1.5-2 times), is associated with the pinning of the magnetic moments on the nanopore edges. Application of the Stoner-Wohlfarth model for fitting the experimental M/M-S(H) curves yielded clear evidence of the predominantly coherent rotation mechanism of magnetization reversal in the porous films. (C) 2017 Elsevier B.V. All rights reserved.