We explore two different problems in string theory in which duality relates an ordinary p-form field in one theory to a self-dual (p+1)-form field in another theory. One problem involves comparing D4-branes to M5-branes, and the other involves comparing the Ramond-Ramond forms in type-IIA and type-IIB superstring theory. In each case, a subtle topological effect involving the p-form can be recovered from a careful analysis of the quantum mechanics of the self-dual (p+1)-form.