We describe a practical procedure for analytically continuing a scattering matrix element into the complex angular momentum plane, given its values at the physical angular momentum quantum numbers of 0, 1, 2,.... The procedure first applies a preconditioning function to the scattering matrix element; then the remaining residual function is interpolated using Fade approximations. The method is illustrated by extracting the leading Regge pole position and residue for the state selected reactions Cl + HCl(upsilon = 1, j = 5) --> ClH(upsilon' = 1, j' = 5) + Cl and I + HI(upsilon = 0, j = 0) --> IH(upsilon' = 0, j' = 2) + I, where upsilon and j are vibrational and rotational quantum numbers respectively.