This paper proposes new discretization methods of continuous-time controllers in which the error between the continuous-time control system and the discretized control system is suppressed in the sense of sampled-data systems. The basic idea is to discretize the continuous-time controller in two steps. In the first step, we determine numerically what frequency response characteristics are desirable for the discretized controller to assume, based on the frequency response gain or H∞ norm of sampled-data systems. Then, in the second step, a discrete-time controller is designed that achieves the desirable frequency response characteristics as close as possible, again with a numerical optimization method. Two independent approaches called the open-loop scheme and the closed-loop scheme are proposed based on this idea, both of which aims at suppressing the performance deterioration from the viewpoint of closed-loop control systems. For each of these schemes, reasonable frequency weights for the associated optimization problems are given. A numerical example is also given to demonstrate the effectiveness of the proposed methods.