The correlated electronic structure of the submonolayer surface systems Sn/Si(111) and Sn/Ge(111) is investigated by density-functional theory and its combination with explicit many-body methods. Namely, the dynamical mean-field theory and the slave-boson mean-field theory are utilized for the study of the intriguing interplay between structure, bonding, and electronic correlation. In this respect, explicit low-energy one- and four(-like)-band models are derived using maximally localized Wannier(-type) functions. In view of the possible low-dimensional magnetism in the Sn submonolayers we compare different types of magnetic orders and indeed find a noncollinear ordering to be stable in the ground state. With single-site methods and cellular-cluster extensions the influence of a finite Hubbard on the surface states in a planar and a reconstructed structural geometry is furthermore elaborated.