The paper presents a study of the effects of a simulated L- to H-mode transition for the proposed BPX (Burning Plasma Experiment) device on the coupling of a recessed coil antenna in the ion cyclotron range of frequencies. Two computer codes are used: ANTIMP, a code developed by the authors, which uses a Runge-Kutta method of solution, and a finite element code, developed by Brambilla, which has been modified to examine fourfeed antenna coils. The radiation resistance is calculated for antenna parameters consistent with a design proposed by the Oak Ridge National Laboratory. Both finite cavity size and finite phase velocity along the current straps are modelled. The plasma density is simulated using both piecewise linear profiles and parabolic profiles. For anticipated BPX values of the density gradient at the separatrix, the radiation resistance decreases by a factor of two to three during an L- to H-mode transition. The reduction of the value of the radiation resistance due to finite phase velocity can be minimized by using a four-feeder scheme.