The velocity observer in Wondergem et al. [2011] ("the Wondergem Observer") and the velocity observer in Stamnes et al. [2011] ("the Stamnes Observer") are evaluated and compared for a ship model given in Wondergem et al. [2011]. The former observer has shown to be uniformly semi-globally exponentially stable. The latter observer has proven to be uniformly globally asymptotically stable and semi-globally exponentially stable when certain requirements are satisfied. However, due to a non-linear damping term in the ship model, the Stamnes Observer only meets the conditions for uniformly semi-globally exponentially stability.The two observers have shown different convergence properties. The Wondergem Observer has a large overshoot during the settling period, then follows the reference robustly. The Stamnes Observer has a first order system behaviour and can become underdamped in the position convergence. Both observers show similar behaviour when considering a bias in the system equations. However, the run time for the Stamnes observer when simulating on a desktop computer is one to two orders of magnitude longer than for the Wondergem Observer.From the evaluations in this thesis, the Wondergem Observer has shown to be the best choice for the given ship model. It is more robust than the Stamnes Observer, it does not have a lower degree of stability as first implied, and it has a much simpler structure.