We will discuss two maps that naturally arise in study of the cohomology of number fields with ramification restricted to a finite set S of primes. By comparing them, we can relate the cokernel of one of them, an S-reciprocity map, to the dual Selmer groups of residual representations for newforms that satisfy congruences with Eisenstein series modulo a prime in S. This allows us to prove something of a main conjecture for these Selmer groups (and, in fact, their pseudo-cyclicity) under hypotheses that include Greenberg’s conjecture.