In this paper, we consider minimax nondifferentiable fractional programming problems with data uncertainty in both the objective and constraints. Via robust optimization, we establish the necessary and sufficient optimality conditions for an uncertain minimax convex-concave fractional programming problem under the robust subdifferentiable constraint qualification. Making use of these optimality conditions, we further obtain strong duality results between the robust counterpart of this programming problem and the optimistic counterpart of its conventional Wolf type and Mond-Weir type dual problems. We also show that the optimistic counterpart of the Wolf type dual of an uncertain minimax linear fractional programming problem with scenario uncertainty (or interval uncertainty) in objective function and constraints is a simple linear programming, and show that the robust strong duality results in sense of Wolf type always hold for this linear minimax fractional programming problem.