We study the A-stability and accuracy characteristics of Clenshaw-Curtis collocation and present closed-form expressions to evaluate the Runge-Kutta coefficients of these methods. The stability study proves that these methods are A-stable up to a high number of nodes. High accuracy is another benefit of these methods; numerical experiments demonstrate that they can match the accuracy of the Gauss-Legendre collocation, which has the optimal accuracy order of all Runge-Kutta methods.