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 betwen the two stable states, both for fixed N and in the limit when N tends to infinity. These estimates would be the main step for a rigorous understanding of the metastable behavior of infinite dimensional systems, as the stochastically perturbed Ginzburg-Landau equation. The quantities of interest are objects of potential theory, as capacities and equilibrium measure. We prove estimates with error bounds that are uniform in the dimension of the system.