This paper considers a general class of varying coefficient models defined by a set of moment equalities and/or inequalities, where unknown functional parameters are not necessarily point-identified. We propose an inferential procedure for a subvector of the varying parameters and establish the asymptotic validity of the resulting confidence sets uniformly over a broad family of data-generating processes. We also propose a practical specification test for a set of necessary conditions of models considered in this paper. Monte Carlo studies show that the proposed methods have good finite sample properties. We apply our method to estimate the return to education using part of the year 2005 1%-population census data from China.