Proteins are the primary agents of function in biological systems, and their levels are critical control elements, reflecting the interplay between transcription, translation, and protein degradation. Here, we consider the role of microRNAs (miRNAs) in the post-transcriptional regulation of protein synthesis. To determine their impact on protein concentration, we constructed a mechanistic model consisting of four state variables and nine kinetic parameters that account for transcript sequestration and degradation via miRNA-mRNA complex formation. Our dynamical model predicts that, even when present in low copy number, miRNAs can exert potent effects on protein concentration. Sensitivity analysis of the steady-state solution indicates that miRNA synthesis commonly acts to fine-tune protein concentrations. However, the same analysis shows that for a small subset of miRNA-mRNA pairs characterized by slowly produced miRNAs, the miRNA synthesis rate is the dominant control element. Our model equations provide a tool to evaluate the importance of particular miRNAs on their target proteins and promote the development of miRNA-based therapies that target proteins associated with cancer, inflammation, and metabolic disorders.