The damping behavior of bent fiber near-field scanning optical microscopy (NSOM) probes operating in tapping mode oscillation is investigated in air and water. We show that the significant drop in probe quality factor Q, which occurs at the air-water interface, is due to meniscus damping. As the probe is immersed in water viscous damping adds to the meniscus damping. Damping effects which lead to a progressive drop in the peak tapping mode resonance frequency are accounted for by additional torsional modes of probe vibration. Understanding the damping processes should lead to the design of high sensitivity NSOM probes for scanning soft biological samples under liquid.