In the paper we investigate central polynomials for the matrix algebra with symplectic involution *. Their form is inspired by an approach of Formanek and Bergman for investigating matrix identities by means of commutative algebra. We find a necessary condition for the existence of central polynomials of the considered type and define their minimal degree. A description of such central polynomials forM4(K.*) is given. Some investigations are made forM6(K.*).