Drops of normal alkanes (CH3(CH2)nCH3, n = 7-14) were confined to specific, geometrically defined areas of a surface by patterning the surface with wetting and nonwetting regions. Each region of the surface comprised a self-assembled monolayer (SAM) of an alkanethiolate on gold, with wettable regions formed from CH3NHCO(CH2)15SH and nonwetting regions formed from CF3(CF2)9(CH2)2SH. The asymmetric shapes formed by the geometrically confined drops of liquid were calculated using a finite element analysis that minimized the excess surface free energy and gravitational potential energy of the drop. A calculation started with the area and shape of the wettable region of the surface, the volume of the drop, the liquid-vapor free energy, gamma(lv), and an assumed value of the difference between the solid-vapor and solid-liquid interfacial free energies, gamma(sv) - gamma(sl). The value of gamma(sv) - gamma(sl) was adjusted iteratively to fit calculated drop shapes to experimental drop shapes. This combination of experiment and numerical analysis forms the basis of a new method to estimate values of gamma(sv) - gamma(sl) (and thus, using these values, to calculate the contact angles, theta, that would be observed for unbounded drops) for liquids on organic surfaces. Estimates of theta in the range 15-degrees < theta < 30-degrees were confirmed using a conventional optical telescope and goniometer; estimates in the range 3-degrees < theta < 15-degrees were beyond the resolution of the telescope and goniometer.