© 2019 American Physical Society. We calculate the thermoelectric response coefficients of three-dimensional Dirac or Weyl semimetals as a function of magnetic field, temperature, and Fermi energy. We focus in particular on the thermoelectric Hall coefficient αxy and the Seebeck coefficient Sxx, which are well-defined even in the dissipationless limit. We contrast the behaviors of αxy and Sxx with those of traditional Schrödinger particle systems, such as doped semiconductors. Strikingly, we find that for Dirac materials αxy acquires a constant, quantized value at sufficiently large magnetic field, which is independent of the magnetic field or the Fermi energy, and this leads to unprecedented growth in the thermopower and the thermoelectric figure of merit. We further show that even relatively small fields, such that ωcτ∼1 (where ωc is the cyclotron frequency and τ is the scattering time), are sufficient to produce a more than 100% increase in the figure of merit.