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In the context of (super)conformal field theories extended probes may preserve enough symmetry to put strong constraints on physical observables. We discuss such constraints for a BPS line defect in four-dimensional N=2 superconformal field theories, with a particular focus on supersymmetric Wilson lines. For the latter case our techniques allow to prove a simple non-trivial relation between the energy emitted by a moving particle and the insertion of a stress tensor operator in the defect background. We discuss the existence of such a relation for other defects and we outline its powerful role for exact computations via localization.
