We report on a concept for vapor sensing with the quartz crystal microbalance where the vapor phase is absorbed into small droplets of an ionic liquid. The liquid is contained in the pores of a nanoporous alumina layer, created on the front electrode of the quartz crystal by anodization. Ionic liquids are attractive for vapor sensing because--being liquids--they equilibrate very fast, while at the same time having negligible vapor pressure. Containing the ionic liquids inside cylindrical cavities of a solid matrix removes all problems related to the liquid's softness as well as the possibility of dewetting and flow. The absence of viscoelastic effects is evidenced by the fact that the bandwidth of the resonance remains unchanged during the uptake of solvent vapor. The Henry constants for a number of solvents have been measured.