  Energy momentum tensors of higher-derivative free scalar conformal field
theories in flat spacetime are discussed. Two algorithms for the computation of
energy momentum tensors are described, which accomplish different goals: the
first is brute-force and highlights the complexity of the energy momentum
tensors, while the second displays some features of their geometric origin as
variations of Weyl invariant curved-space actions. New compact expressions for
energy momentum tensors are given and specific obstructions to defining them as
conformal primary operators in some spacetime dimensions are highlighted. Our
discussion is also extended to higher-derivative free spinor theories, which
are based on higher-derivative generalizations of the Dirac action and provide
interesting examples of conformal field theories in dimension higher than two.
