What did a posthumous consulship achieve?

Did being named consul after death benefit the man's family, or was it only an honorary title?

It was chiefly honorary, but it gave the family additional ancestral prestige that descendants could use in Roman politics.

The honor gave the dead officer a title and his descendants a source of prestige. A consul suffectus normally filled a vacancy left when an elected consul died or otherwise left office before the year ended. Scaurus's posthumous award functioned as an exceptional tribute to the reputation Rome chose to preserve. In an aristocratic political culture built around ancestral offices and military distinction, later family members could present the appointment as evidence of exceptional service. The title did not change the dead man's fate, but it could materially improve the family's political story.