The paradox of relatively error free function in biological systems composed of relatively error prone components has recently come under intensive investigation. In the case of tRNA aminoacylation, aminoacyl-tRNA synthetases were discovered to have a separate function that allows misacylated molecules to be hydrolyzed more rapidly than correctly acylated molecules. This additional function of the synthetases provides a proofreading or verification mechanism that is believed to improve significantly the overall accuracy of tRNA aminoacylation. In this paper we provide an explicit relationship between the accuracy achieved by proofreading and the energy cost. Experimental data available in the literature are examined in light of this relationship. The following are the principal conclusions from our study: (1) high-accuracy proofreading of tRNA aminoacylation has a high energy cost, as much as 100 times greater than indications from early experimental work; (2) the minimum net error derived in previous theoretical studies is never actually reached; (3) mechanisms in which misacylation and subsequent proofreading occur on the surface of the same synthetase molecule achieve a much higher accuracy than mechanisms in which these functions occur on the surface of different synthetase molecules.