nlm = NonlinearModelFit[data, {x^a Cos[b x + c]}, {a,b,c} ,{x}]

params = nlm["BestFitParameters"]
(* a -> 0.0203318, b -> 3085.99, c -> 30.1162} *)

models = {nlm, ...}
Table[models[[i]]["BestFitParameters"],{i,1,Length[models]}]

a = {1, 2, 3, 4};
a /. x_ :> x^2
(* {1, 4, 9, 16} *)