The Shockley surface state on Cu(111) reacts sensitively to the perturbation by molecular adsorbates on the surface. In the porous structure of a metal-coordinated molecular network on Cu(111), the surface state is confined to a series of discrete states. Energy and momentum of eigenstates in the pores are related to both the energy dispersion of the free surface state and the geometric and energetic details of the confining barrier formed by the molecular network. The penetration of the confined state into the barrier is found to be sensitive to the constituting architectural elements.