We extend standard tools from equilibrium refinement theory in non-cooperative games to a cooperative framework of network formation. First, we introduce the new concept of perfect pairwise stability. It transposes the idea of “trembling hand” perfection to network formation theory and strictly refines the pairwise stability concept of Jackson and Wolinsky (1996). Second, we study basic properties of perfect pairwise stability: existence, admissibility and perturbation. We further show that our concept is distinct from the concept of strongly stable networks introduced by Jackson and Van den Nouweland (2005), and perfect Nash equilibria of the Myerson network formation game studied by Calvó-Armengol and İlkılıç (2009). Finally, we apply perfect pairwise stability to sequential network formation and prove that it enables a refinement of sequential pairwise stability, a natural analogue of subgame perfection in a setting with cooperative, pairwise link formation.