We　analyze　the　optimal　global　and　local　convergence　properties　of　continuous　Galerkin　(CC)　solutions　on　quasi-geometric　meshes　for　delay　differential　equations　with　proportional　delay.　It　is　shown　that　with　this　type　of　meshes　the　attainable　order　of　nodal　superconvergence　of　CG　solutions　is　higher　than　of　the　one　for　uniform　meshes.　The　theoretical　results　are　illustrated　by　a　broad　range　of　numerical　examples.