Phobic droplet-fiber systems possess complex geometries, which have made full characterization of such systems difficult. This work has used atomic force microscopy (AFM) to measure droplet-fiber forces for oil droplets on oleophobic fibers over a range of fiber diameters. The work adapted a previous method and a theoretical model developed by the authors for philic droplet-fiber systems. A Bayesian statistical model was also used to account for the influence of surface roughness on the droplet-fiber force. In general, it has been found that the force required to move a liquid droplet along an oleophobic filter fiber will be less than that required to move a droplet along an oleophilic fiber. However, because of the effects of pinning and/or wetting behavior, this difference may be less than would otherwise be expected. Droplets with a greater contact angle (similar to 110 degrees) were observed to roll along the fiber, whereas droplets with a lesser contact angle (<90 degrees) would slide.