Summary: The goal of this paper is to investigate the Tikhonov-Phillips method for semi-discrete linear ill-posed problems in order to determine tight error bounds and to obtain a good parameter choice. We consider the equation \(Af = g\), where the operator \(A\) is known, noisy discrete data \(g_1^\delta ,\dots , g_n^\delta \) with \(g(x_i)\approx g_i^\delta \) can be observed and a solution \(f^*\) is sought. Assuming that \(f^*\) is an element of a Sobolev space, we use the well-known theory of optimal recovery in Hilbert spaces for the reconstruction process. We then provide \(L_{2}\)-error estimates in terms of the data density and derive an a priori selection for the regularization parameter, which guarantees an optimal compromise between approximation and stability. Finally, we illustrate the parameter selection with a simple example.