The fact that genes compete for shared cellular resources poses a fundamental challenge when identifying parameters of genetic parts. A recently developed model of gene expression tackles this problem by explicitly accounting for resource competition. In addition to accurately describing experimental data, this model only depends on a small number of easily identifiable parameters with clear physical interpretation. Based on this model, we outline a procedure to select the optimal set of experiments to characterize biomolecular parts in synthetic biology. Additionally, we reveal the role competition for shared resources plays, provide guidelines how to minimize its detrimental effects, and how to leverage this phenomenon to extract the most information about unknown parameters. To illustrate the results, we consider the case of part characterization in cell-free extracts, treat plasmid DNA concentrations as decision variables, and demonstrate the significant performance difference between naive and optimal experiment design.