Spectral estimation is the task of finding the power associated with a signal across the frequency range of the signal. In classical signal processing applications, this is a solved problem when the time series is fully observed and equally spaced in time. However, in many cases, there are either missing observations, or the data is unevenly spaced in time. Here, probabilistic methods can be extremely valuable, as we can use nonparametric methods to provide better interpolation of the frequency domain, whilst handling the uncertainty in a principled way. This paper proposes a method to tackle this problem, with exact inference.