Elucidating compensatory mechanisms underpinning phonemic fluency (PF) may help to minimize its decline due to normal aging or neurodegenerative diseases. We investigated cortical brain networks potentially underpinning compensation of age-related differences in PF. Using graph theory, we constructed networks from measures of thickness for PF, semantic, and executive–visuospatial cortical networks. A total of 267 cognitively healthy individuals were divided into younger age (YA, 38–58 years) and older age (OA, 59–79 years) groups with low performance (LP) and high performance (HP) in PF: YA-LP, YA-HP, OA-LP, OA-HP. We found that the same pattern of reduced efficiency and increased transitivity was associated with both HP (compensation) and OA (aberrant network organization) in the PF and semantic cortical networks. When compared with the OA-LP group, the higher PF performance in the OA-HP group was associated with more segregated PF and semantic cortical networks, greater participation of frontal nodes, and stronger correlations within the PF cortical network. We conclude that more segregated cortical networks with strong involvement of frontal nodes seemed to allow older adults to maintain their high PF performance. Nodal analyses and measures of strength were helpful to disentangle compensation from the aberrant network organization associated with OA.