In previous papers, the authors have designed a divergence-free WKB asymptotic method for differential equations that yields a WKB approximation of the solution of that differential equation free from divergence for any real value of the asymptotic variable, even around the classical turning point. In this paper the authors claim that any WKB method for differential equations can be translated in one-to-one manner to the corresponding steepest descent method for integrals. In fact, in this paper the authors present a steepest descent method that corresponds to the above mentioned divergence-free WKB method previously designed by the authors. From this one-to-one translation, the authors notice that the key to convert the traditional steepest descent method for integrals into a divergence-free method is the choice of integration variable in the integral.