The chloroplast and mitochondrion are often uniparentally inherited, so the inferred relationships between the organelles should be concordant. However, several recent studies have found that some plant clades exhibit biparental inheritance of the organelles. Therefore, the two organelles have the potential to exhibit conflicting topologies. This study examines four cases where phylogenetic conflict between organelles has been reported. Using a series of phylogenetic tests, we investigate whether this conflict reflects evolutionary history or results from limitations in phylogenetic methods.