Abstract
We investigate the constraints that OH microwave transitions in megamasers and molecular absorbers at cosmological distances may place on the evolution of the fine structure constant alpha=e^2/(hbar c). The centimeter OH transitions are a combination of hyperfine splitting and lambda-doubling that can constrain the cosmic evolution of alpha from a single species, avoiding systematic errors in alpha measurements from multiple species which may have relative velocity offsets. The most promising method compares the 18 and 6 cm OH lines, includes a calibration of systematic errors, and offers multiple determinations of alpha in a single object. Comparisons of OH lines to the HI 21 cm line and CO rotational transitions also show promise.

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