This paper presents a min-max interpolation method for the nonuniform fast Fourier transform (NUFFT) that minimizes the worst-case approximation error over all unit-norm signals. The method is derived from first principles and is applicable to both one-dimensional and multidimensional signals. The authors show that their approach provides significantly lower approximation errors compared to 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 includes numerical results demonstrating the improved accuracy of the min-max NUFFT method and discusses its extensions, including shifted signals, adaptive neighborhoods, and reduced FFT. The authors also analyze the error analysis of conventional shift-invariant interpolation methods and compare their performance with the min-max approach.This paper presents a min-max interpolation method for the nonuniform fast Fourier transform (NUFFT) that minimizes the worst-case approximation error over all unit-norm signals. The method is derived from first principles and is applicable to both one-dimensional and multidimensional signals. The authors show that their approach provides significantly lower approximation errors compared to 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 includes numerical results demonstrating the improved accuracy of the min-max NUFFT method and discusses its extensions, including shifted signals, adaptive neighborhoods, and reduced FFT. The authors also analyze the error analysis of conventional shift-invariant interpolation methods and compare their performance with the min-max approach.