The capping inversion of the marine boundary layer is often associated with ducted microwave propagation which can significantly impact shipboard radars. This paper concerns the problem of characterizing ducted propagation by estimating parameters of the index of refraction profile using radar sea clutter returns. Specifically, a maximum a posteriori (MAP) estimate is proposed for determining duct height and its first-order range-dependence under conditions of uncertain slowly range-varying surface backscatter cross-section. In addition, a fast recursively-computed hybrid Cramer-Rao bound on refractivity estimation is developed. Finally, real data refractivity estimation results are presented using radar clutter returns collected off the Virginia coast. Preliminary refractivity estimates compare favorably with measurements made using helicopter-borne instruments out to a range of approximately 50 km.