The silks of Orb-Weaver spiders (family Araneidae) are emerging as fascinating optical materials due to their biocompatibility, ecological sustainability and mechanical robustness. Natural spider silks are mainly spun as double cylinders, with diameters ranging from 0.05 to 10 μm, depending on the species and maturity of the spider. This small size makes the silks difficult to characterize optically with traditional techniques. Here, we present a technique that is capable of measuring both the real and imaginary refractive index components of spider silks. This technique is also a new capability for characterizing micro-optics more generally. It is based on the measurement and analysis of refracted light through the spider silk, or micro-optic, while it is immersed in a liquid of known refractive index. It can be applied at any visible wavelength. Results at 540 nm are reported. Real refractive indices in the range of 1.54-1.58 were measured, consistent with previous studies of spider silks. Large silk-to-silk variability of the p-polarized refractive index was observed of around 0.015, while variability in the s-polarized refractive index was negligible. No discernible difference in the refractive indices of the two cylinders making up the double cylinder silk structure were observed. Measured imaginary refractive indices corresponded to an optical loss of around 14 dB/mm at 540 nm.