In this thesis, we study different methods of likelihood estimation in a Cox proportional hazards model in a nested case-control study. To be more specific, how they deal with the problem of overmatching. This problem has long been known as a pitfall in regular matched case-control studies. It is in this thesis translated into a nested case-control setting with additional matching. This translation gives us two different situations based on the association the additional matching variable has on the outcome. Both situations of overmatching rely on the matching variable and an exposure variable is highly correlated, so that one partially match on the exposure. Through a series of Monte Carlo simulations, three different inverse probability weighted estimation methods are compared with the estimation method traditionally used in these kinds of studies. This is then followed by an application on a real dataset. The results of the analysis rests heavily on the matching variable's association with the outcome. When this has an association on its own, the gain in using weighted estimation methods in estimating the effect of the exposure, is modest. This modest effect is however not true if one wishes to estimate the effect of the matching variable as well. The weighted methods are also better than the traditional method when there is overmatching with no association between matching variable and outcome. Finally, we may have stumbled upon a problem with the regression-based weights in some situations.