When investigating the linear stability properties of an implicit Runge- Kutta method, the method is applied with stepsize \(h\) to the scalar test equation \(y' = qy\), \(Re(q) < 0\). It is well known that the linear stability properties of a Runge-Kutta method are determined solely by the stability properties of the associated rational approximation to the exponential. It is also well known that the Padé approximation \(R_{n,m} = N_{n,m}(z) / M_{n,m}(z)\) to the exponential function \(\text{exp}(z)\) where \(N_{n,m}(z)\) is of degree \(n\) and \(M_{n,m}(z)\) is of degree \(m\), is \(A\)-stable if and only if \(0 \leq m-n \leq 2\) [cf. \textit{B. L. Ehle}, SIAM J. Math. Anal. 4, 671-680 (1973; Zbl 0236.65016)]. In studying the linear stability properties of a broader class of general linear methods one must generalize these rational approximations. The authors present a method of constructing these approximations for arbitrary order and degree. In the case of quadratic Padé approximations a generalization of the Ehle inequality is both necessary and sufficient for \(A\)-stability. In the case of cubic Padé approximations, however, the inequality is shown to be insufficient for \(A\)-stability. Finally the authors give an example of the construction of a general linear method whose stability region corresponds to a given generalized quadratic Padé approximation.