Matlab functions to work with the canonical structures for congruence and *congruence of matrices, and for congruence of symmetric and skew-symmetric matrix pencils are presented. A user can provide the canonical structure objects or create (random) matrix example setups with a desired canonical information, and compute the codimensions of the corresponding orbits: if the structural information (the canonical form) of a matrix or a matrix pencil is known it is used for the codimension computations, otherwise they are computed numerically. Some auxiliary functions are provided too. All these functions extend the Matrix Canonical Structure Toolbox.