This paper investigates the relationship between inflation and inflation uncertainty in twelve EMU countries. A time-varying GARCH model is estimated to distinguish between short-run and steady-state inflation uncertainty. The effects of the introduction of the Euro in 1999 are then examined introducing a dummy variable. Overall, it appears that post-1999 steady-state inflation has generally remained stable, steady-state inflation uncertainty and inflation persistence have both increased, and the relationship between inflation and inflation uncertainty has broken down in many countries. When the break dates are determined endogenously, the adjustment is found to have taken place before the introduction of the Euro.