In a Cox regression model, instability of the estimated regression coefficients can be reduced by maximizing a penalized partial log-likelihood, where a penalty function of the regression coefficients is substracted from the partial log-likelihood. In this paper, we choose the optimal weight of the penalty function by maximizing the predictive value of the model, as measured by the crossvalidated partial log-likelihood. Our methods are illustrated by a study of ovarian cancer survival and by a study of centre-effects in kidney graft survival.