We consider a coupled bistable N-particle system driven by a Brownian noise, with a strong coupling corresponding to the synchronised regime. Our aim is to obtain sharp estimates on the metastable transition times between the two stable states, both for fixed N and in the limit when N tends to infinity, with error estimates uniform in N. These estimates are a main step towards a rigorous understanding of the metastable behavior of infinite dimensional systems, such as the stochastically perturbed Ginzburg-Landau equation. Our results are based on the potential theoretic approach to metastability.