Some studies, most of them case-reports, suggest that synesthetes have an advantage in visual search and episodic memory tasks. The goal of this study was to examine this hypothesis in a group study. In the present study, we tested thirteen grapheme-color synesthetes and we compared their performance on a visual search task and a memory test to an age-, handedness-, education-, and gender-matched control group. The results showed no significant group differences (all relevant ps$>$.50). For the visual search task effect sizes indicated a small advantage for synesthetes (Cohen’s d between .19 and .32). No such advantage was found for episodic memory (Cohen’s d$<$.05). The results indicate that synesthesia per se does not seem to lead to a strong performance advantage. Rather, the superior performance of synesthetes observed in some case-report studies may be due to individual differences, to a selection bias or to a strategic use of synesthesia as a mnemonic. In order to establish universal effects of synesthesia on cognition single-case studies must be complemented by group studies.