The construction and evaluation of rational polynomials that interpolate Hermite data are addressed. The authors prefer the so-called barycentric form for stability and computational efficiency. They emphasize the choice of the denominator polynomial, which is treated as a free parameter in order to obtain additional accuracy over the range of interpolation; the numerator is of sufficient degree to allow polynomial interpolation. Through suitable choice of the denominator it is possible to obtain small errors even at the extremities of the interval of interpolation, although at the cost of some increase of errors near the center of the interval. Issues such as stability and computational efficiency are addressed; this discussion is useful for those who wish to use the scheme in applications.