We study the limits of (∞, 1)-categories with structure and the lax morphisms between them by introducing the notion of enhanced simplicial categories. We establish that many interesting enhanced simplicial categories, including that of (∞, 1)-categories with limits, and that of Cartesian fibrations between (∞, 1)-categories, admit several kinds of weighted limits that involve lax morphisms in the diagrams, such as Eilenberg-Moore objects over monads that are lax morphisms, and ∞-categorical versions of equifiers and inserters whose diagrams involve lax morphisms. Our results specialise to any model for (∞, 1)-categories, therefore generalising results in quasi-categories and also categories.