In this paper, we propose a novel estimator of the instantaneous frequencies (IFs) of the modes making up multicomponent signals (MCSs). We are particularly interested in dealing with noisy MCSs containing close modes in the time-frequency plane. Though it is possible to adapt Prony approach to estimate IFs in such situations, interference between the modes generates oscillations in the obtained estimations. After having investigated the nature of these oscillations, we propose an algorithm to remove these in IFs estimation, based on spline approximation. Numerical applications in various situations illustrate the benefit of mixing Prony technique with spline approximation for IF estimation in noisy MCSs containing close modes.