The problem is considered of fitting a stable rational transfer function to complex frequency response data minimizing a weighted maximum amplitude criterion. A solution for this problem is provided in both discrete and continuous time and for both SISO and MIMO systems by parametrizing the transfer function and solving a smooth nonlinear constrained optimization problem. The denominator is parametrized as a product of first and second-order polynomials. By adding linear constraints on the denominator parameters to the nonlinear programming problem the poles of the curve fit model are restricted to the stability region in the complex plane. To provide an initial estimate for the nonlinear optimization problem an iterative procedure is proposed where, in each step, a linear programming problem has to be solved.