An atomic force microscope (AFM) is used to investigate changes in the effective viscosity of liquids which are confined between an AFM tip and a sample surface. In both cases studied, namely octamethylcyclotetrasiloxane near graphite and water near mica, it is found using two methods that the damping increases markedly at small tip-sample separations (<20 Angstrom), even for sharp tips. The strong change in damping with tip-sample separation allows the AFM feedback to be controlled in noncontact mode (i.e., off the surface). Hence, the increase in damping can be directly associated with changes in the material properties of the confined liquid.