In this study, the problem of amplitude estimation of (inter)harmonics is investigated. Specifically performance limits are provided for the accuracy of unbiased amplitude estimation algorithms and for the analysis window size required by an algorithm for achieving and maintaining a desired accuracy. Cramer-Rao lower bound (CRLB) is used for the bounds on the accuracy. Unlike the existing literature concentrating on the asymptotic behaviour of the bounds, the behaviour of CRLBs for small window sizes and close frequency components is investigated. In particular, the (worst) amplitude CRLBs are shown to be inversely proportional to the squared frequency differences for small analysis window sizes and close frequency components. For the bounds on analysis window size, the concept of convergence-time is defined and illustrated. The convergence-times of unbiased amplitude estimation algorithms are then lower bounded by establishing its relationship with CRLBs. The results and ideas are illustrated using both synthetic signals and field data collected from a power grid. Numerical results show that the proposed performance limits are tight and have strong prediction capabilities for amplitude estimation algorithms having prior knowledge about the existing frequencies in the signal.