<p>This paper is devoted to studying conformal algebras of quotients of Lie conformal algebras. The notions of conformal algebras of quotients of Lie and associative conformal algebras are introduced and some necessary and sufficient conditions about their conformal algebras of quotients are developed. Moreover, many properties of conformal algebras of quotients are also investigated. Besides, the maximal conformal algebra of quotients of every semi-prime Lie conformal algebra is constructed. Moreover, for any two associative conformal algebras, the relation of ‘quotients’ can be inherited by Lie conformal algebras generated by them.</p>