Grand canonical Monte Carlo simulations were carried out for the estimation of the two-phase equilibrium of methane in narrow-slit pores with wetted walls. The pore width varied from 4 up to 12 molecular diameters, and the systems were investigated at 111.1 K. It was shown that fdr the graphite-like pores the vapor-liquid coexistence at the concave meniscus existed for pore widths not less than 10 molecular diameters. For the weaker adsorbate-adsorbent potential, vapor-liquid coexistence was found for the smaller values of pore widths. The dependence of the surface tension of the concave meniscus on its curvature was estimated.