Certificates are useful when it comes to verifying an extensive algorithm with its implementation. The Fréchet distance between two curves indicates how similar they are and is further the problem under consideration for this thesis. Therefore, certification algorithms will be developed to find out how far the reference algorithm is from an optimal solution for computing the Fréchet distance. To do so, the effects of particularly short certificates determined by this works' algorithms are evaluated. Additionally, a benchmark using real world data was used and further adapted, providing information about the actual improvement of this work compared to the reference in terms of the size of certificates.