We present an efficient method for computing resonance fields for cw EPR that adaptively models the state energies over a given field range with cubic splines. The method diagonalizes the spin Hamiltonian matrix for suitably chosen fields, which are determined by an adaptive iterative bisection procedure. Resonance fields are computed from the cubic spline model. The new method adapts to the complexity of the spin system and keeps the number of diagonalizations minimal. For systems with field-independent interactions (FII) small compared to the spectrometer frequency v(0) only three diagonalizations are needed, for high-spin systems with FII larger than v(0) up to 60 diagonalizations are necessary. (C) 2003 Elsevier B.V. All rights reserved.