Microsolvation of ions is a subject of active explorations pursuing the objectives of understanding microscopic details of ion solvation in bulk solutions. In the present work core ionization of positively charged microsolvated clusters is addressed. This research area did not receive much attention so far. The Na 1s(-1) core ionization spectra of Na(+)(H(2)O)(n) and Na(+)(NH(3))(n) clusters have been calculated by means of an accurate ab initio Green's function method. Various dependencies of the core ionization energy on the number of solvent molecules, their arrangement, and chemical type are investigated and explained. Special emphasis is also given to the low-energy parts of the calculated core ionization spectra that exhibit numerous shake-up satellites mostly originating from the transfer of electrons from the solvent molecules to the Na(+) ion induced by core ionization. Spectral characteristics of selected charge-transfer satellites are discussed in detail.