High-field electron paramagnetic resonance (EPR) is used to investigate two magnetically concentrated II1-xMnxVI alloys, Cd1-xMnxSe and Cd1-xMnxSe, for x≫0.15. Earlier EPR studies carried out between 9.0 and 35 GHz had shown that the EPR linewidths in II1-xMnxVI alloys are determined by anisotropic Dzyaloshinskii-Moriya superexchange. However, broadening of the resonance prevented those early EPR studies to be performed at high Mn concentration x and low temperature T, i.e., precisely when II1-xMnxVI systems become magnetically most interesting. We circumvent this problem by performing EPR measurements at high magnetic fields, using frequencies between 95 and 380 GHz. In addition to information on resonance broadening, the ability to measure EPR at very high x and low T (i.e., when the magnetic moments are very strongly coupled) revealed significant shifts of the resonance from the EPR position of Mn++ ions. We tentatively ascribe these shifts to internal fields produced by the spin sublattice within the II1-xMnxVI alloy.