In this talk we will discuss some extremal problems related to embeddings between weighted Paley–Wiener spaces. We will present some asymptotic results for sharp constants in terms of the parameters involved, deduce existence results for extremal functions as well as radial symmetry of those, and talk about some numerical results. For certain cases, these extremal problems can be reformulated in terms of sharp Poincaré inequalities, and for those cases we will present a characterisation of extremizers and sharp constants that recover several classical results.