The director fields adopted by nematic liquid crystals (LCs) that are confined by the surface to form long, thin droplets are investigated using polarising optical microscopy. Samples are produced by de-wetting of the LC on a surface patterned with alternating high-surface energy and low-surface energy stripes of 10–30 μm width. The droplets obtained are expected to adopt a profile which is that of a longitudinal section of a cylinder and, as this suggests, the director fields observed are variants in the case where the LC is constrained in a cylindrical capillary or fibre. Hence, when there is normal anchoring at the air interface, the textures observed are related to the well-known escaped radial texture (for the nematic LC mixture E7) or plane polar texture (for the LC mixture MLC6609). More surprising is the observation that the nematic LC mixture MLC7023, which is anchored in a planar or tilted manner at the air interface, also gives what appears to be an escaped radial director field. As an exploration of the possibility of using these systems in creating sensors, the effects of adding a chiral dopant and of adding water to the substrates are also investigated.