Understanding mechanisms of coevolution between nuclear and mitochondrial (mt) genomes is a defining challenge in eukaryotic genetics. The angiosperm genus Silene is a natural system to investigate the causes and consequences of mt mutation rate variation because closely related species have highly divergent rates. In Silene species with fast-evolving mtDNA, nuclear genes that encode mitochondrially targeted proteins (N-mt genes) are also fast-evolving. This correlation could indicate positive selection to compensate for mt mutations, but might also result from a recent relaxation of selection. To differentiate between these interpretations, we used phylogenetic and population-genetic methods to test for positive and relaxed selection in three classes of N-mt genes (oxidative phosphorylation genes, ribosomal genes, and “RRR” genes involved in mtDNA recombination, replication, and repair). In all three classes, we found that species with fast-evolving mtDNA had: 1) elevated dN/dS, 2) an excess of nonsynonymous divergence relative to levels of intraspecific polymorphism, which is a signature of positive selection, and 3) no clear signals of relaxed selection. “Control” genes exhibited comparatively few signs of positive selection. These results suggest that high mt mutation rates can create selection on N-mt genes and that relaxed selection is an unlikely cause of recent accelerations in the evolution of N-mt genes. Because mt-RRR genes were found to be under positive selection, it is unlikely that elevated mt mutation rates in Silene were caused by inactivation of these mt-RRR genes. Therefore, the causes of extreme increases in angiosperm mt mutation rates remain uncertain.