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The resonant tunneling model is the simplest model for describing electronic transport through nanoscale objects like individual molecules. A complete understanding includes not only charge transport but also thermal transport and their intricate interplay. Key linear response observables are the electrical conductance G and the Seebeck coefficient S. Here we present experiments on unspecified resonant tunnel junctions and molecular junctions that uncover correlations between $G$ and $S$, in particular rigid boundaries for $S(G)$. We find that these correlations can be consistently understood by the single-level resonant tunneling model, with excellent match to experiments. In this framework, measuring $I(V)$ and $S$ for a given junction provides access to the full thermoelectric characterization of the electronic system. A remarkable result is that without targeted chemical design, molecular junctions can expose thermoelectric conversion efficiencies which are close to the Carnot limit. This insight allows to provide design rules for optimized thermoelectric efficiency.