Summary: We describe non-trivial \(\delta\)-derivations of semisimple finite-dimensional Jordan algebras over an algebraically closed field of characteristic not 2, and of simple finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic 0. For these classes of algebras and superalgebras, non-zero \(\delta\)-derivations are shown to be missing for \(\delta\neq 0, 1/2, 1\), and we give a complete account of \(1/2\)-derivations.