This paper investigates the interplay between isolated sublattices and closure operators. Isolated sublattices are a special kind of sublattices which can serve to diminish the number of elements of a lattice by means of a quotient. At the same time, there are simple formulae for the relationship between the number of closure operators in the original lattice and the quotient lattice induced by isolated sublattices. This connection can be used to derive an algorithm for counting closure operators, provided the lattice contains suitable isolated sublattices.