The main subject of this thesis is the field of certified system identification. This special kind of identification uses additional information to provide not only the best parameter for fitting data, but also a certificate, which tells how good the estimated parameter is. Therefore, as a first step the classical approach, least squares identification with asymptotic theory, was precisely analysed, in order to develop a feeling for the performance of the common methodology. Later on, a method proposed by Marco C. Campi is presented, for which some beneficial properties have been stated. Since a part of the work was to analyse this method, some test were implemented in simulation, to not only show the functioning, but also proof that the stated properties hold. After analysing both methods separately, a direct comparison of them, where the strengths and weaknesses of each are highlighted, was made. Furthermore the basic idea behind the new approach was used in a different field. It is shown, that one can use this idea to construct an observer for linear systems, which provides not only the estimated state, but additionally a confidence region in the state space, with the same beneficial properties as within for identification. The topic of identification with confidence regions, is strongly related to prediction of future outputs of systems. One chapter of the thesis is dedicated to this subject. The parallelisms and possible wrong interpretations of the connection between these two topics have been analysed and clarified. The obtained results are shown on a practically relevant system, a model for predicting the velocity of a preceding car in city traffic. In the end all developments are summarized and possible starting points for further investigations are shown.