Mutators are popular two-ports, often used for transforming nonlinear resistors into memristors. They can also be used for transforming between various pairs of nonlinear higher-order elements (HOEs) from Chua\'s table. This paper suggests a procedure for the synthesis of Antoniou’s generalized impedance converter (GIC) containing nonlinear HOEs in order to emulate nonlinear elements with prescribed behavior. This approach is demonstrated on emulating the ideal and also extended meminductors.