Time-frequency localization operators (with Gaussian window) were introduced by Daubechies in 1988. Since then they have been studied intensively, in particular regarding boundedness, compactness, Schatten properties and estimates for the eigenvalues. However, sharp estimates for the norm of these operators are still few. In this talk I will present a classical result by Lieb and two new result that give sharp estimates for the norm of localization operators under the assumption that the weight function belongs to one or more $L^p$ spaces.