A unique feature of 5d materials is the fact that spin-orbit coupling, Coulomb interactions, and crystal electric field effects are of comparable strength. In the edge-sharing honeycomb iridates, this competition of energy scales leads to a strongly anisotropic, Ising-like exchange between neighboring isospin-1/2 moments. Such interactions couple each spin to orthogonal components of the three neighboring spins and, as a consequence, no single exchange direction can be simultaneously satisfied, leading to strong frustration closely approximated by the Kitaev Hamiltonian. So far, most potential Kitaev materials have been found to order at low temperatures, eluding the sought-after QSL state. Nonetheless, experiments suggest that Kitaev exchange is the dominant spin interaction in these systems, with additional small contributions from a direct Heisenberg and a symmetric off-diagonal exchange term. We previously showed that a magnetic field completely suppresses the complex incommensurate spiral order in β-Li₂IrO₃, while stabilizing a commensurate zig-zag component similar to the ground state observed in Na₂IrO₃. In this work, we present the magnon excitation spectra of β-Li₂IrO₃ in zero and finite magnetic field, at zone centers corresponding to both coexisting states.