Summary: Some coefficient inverse problems of electromagnetic frequency sounding of inhomogeneous media are considered. Such problems occur in many areas of applied physics, such as the geophysical exploration of gas, oil and mineral deposits, reservoir monitoring, marine acoustics and electromagnetics, optical sensing, and radio physics. Reformulating these problems in terms of nonlinear least squares, also known in the applied literature as matched field processing, often leads to a multiextremal and multidimensional objective function. This makes it extremely difficult to find its global extremum which corresponds to the solution of the original problem. It is shown in this paper that an inverse problem of frequency sounding can first be identically transformed to a certain boundary value problem which does not explicitly contain an unknown coefficient. The nonlinear least squares are then applied to the transformed problem. Using the weight functions associated with the Carleman estimates for the Laplace operator, an objective function is constructed in such a way that it is strictly convex on a certain compact set. The feasibility of the proposed approach is demonstrated in computational experiments with a model problem of magnetotelluric frequency sounding of layered media.