This paper presents a min-max approach for nonuniform fast Fourier transforms (NUFFT), which minimizes the worst-case approximation error over all signals of unit norm. The method is optimal in the min-max sense and generalizes to multidimensional signals. It is shown that the min-max approach provides substantially lower approximation errors than conventional interpolation methods. The min-max criterion is also useful for optimizing the parameters of interpolation kernels such as the Kaiser-Bessel function. The paper discusses the theory of the 1-D case, including the problem statement, min-max interpolator, efficient computation, and various modes of operation. It also extends the method to multidimensional signals and discusses error analysis, including the worst-case error and the effects of different scaling factors. The paper compares the min-max method to conventional methods and shows that optimized scaling factors can significantly reduce error. The results demonstrate that the min-max approach provides accurate and efficient NUFFT computations, particularly for applications such as magnetic resonance imaging and tomography.This paper presents a min-max approach for nonuniform fast Fourier transforms (NUFFT), which minimizes the worst-case approximation error over all signals of unit norm. The method is optimal in the min-max sense and generalizes to multidimensional signals. It is shown that the min-max approach provides substantially lower approximation errors than conventional interpolation methods. The min-max criterion is also useful for optimizing the parameters of interpolation kernels such as the Kaiser-Bessel function. The paper discusses the theory of the 1-D case, including the problem statement, min-max interpolator, efficient computation, and various modes of operation. It also extends the method to multidimensional signals and discusses error analysis, including the worst-case error and the effects of different scaling factors. The paper compares the min-max method to conventional methods and shows that optimized scaling factors can significantly reduce error. The results demonstrate that the min-max approach provides accurate and efficient NUFFT computations, particularly for applications such as magnetic resonance imaging and tomography.