For systems that self-assemble into finite-sized objects, it is sometimes convenient to compute the thermodynamics for a small system where a single assembly can form. However, we show that in the canonical ensemble the use of small systems can lead to significant finite-size effects due to the suppression of concentration fluctuations. We introduce methods for estimating the bulk yields from simulations of small systems and for following the convergence of yields with system size, under the assumptions that the various species behave ideally.