A method of determining the exact coefficient bound, when a polynomial is extended by a single degree, is given. However, this method is unsuitable when additional coefficients with robust bounds are sought. To overcome this, an alternative approach, relying on Kharitonov’s theorem, is used as the basis of an algorithm for determining robust bounds on unknown coefficients in Hurwitz polynomials extended to higher degree. A description of the algorithm implementation and some encouraging results are provided.