We consider spline interpolation problems where information about the approximated function is given by means of interval estimates for the function values over ranges of x-values instead of specific knots. We propose two robust uniyariate spline models formulated as convex semi-infinite optimization problems. We present simplified equivalent formulations of both models as finite explicit convex optimization problems for splines of degrees up to 3. This makes it possible to use existing convex optimization algorithms and software. (C) 2010 Elsevier B.V. All rights reserved.