Context.TheM_BH–σ_⋆relation is considered a result of coevolution between the host galaxies and their supermassive black holes. For elliptical bulge hosting inactive galaxies, this relation is well established, but there is still discussion concerning whether active galaxies follow the same relation.Aims.In this paper, we estimate black hole masses for a sample of 19 local luminous active galactic nuclei (AGNs; LLAMA) to test their location on theM_BH–σ_⋆relation. In addition, we test how robustly we can determine the stellar velocity dispersion in the presence of an AGN continuum and AGN emission lines, and as a function of signal-to-noise ratio.Methods.Supermassive black hole masses (M_BH) were derived from the broad-line-based relations for Hα, Hβ, and Paβemission line profiles for Type 1 AGNs. We compared the bulge stellar velocity dispersion (σ_⋆) as determined from the Ca II triplet (CaT) with the dispersion measured from the near-infrared CO (2-0) absorption features for each AGN and find them to be consistent with each other. We applied an extinction correction to the observed broad-line fluxes and we corrected the stellar velocity dispersion by an average rotation contribution as determined from spatially resolved stellar kinematic maps.Results.The Hα-based black hole masses of our sample of AGNs were estimated in the range 6.34 ≤ logM_BH ≤ 7.75M_⊙and theσ_⋆CaTestimates range between 73 ≤ σ_⋆CaT ≤ 227 km s⁻¹. From the so-constructedM_BH − σ_⋆relation for our Type 1 AGNs, we estimate the black hole masses for the Type 2 AGNs and the inactive galaxies in our sample.Conclusions.We find that our sample of local luminous AGNs is consistent with theM_BH–σ_⋆relation of lower luminosity AGNs and inactive galaxies, after correcting for dust extinction and the rotational contribution to the stellar velocity dispersion.