Desaminotyrosyl-tyrosine ethyl ester (DTE) and desaminotyrosyl-tyrosine (DT) were used as monomers in the synthesis of two tyrosine-derived polycarbonates: the slow degrading homopolymer poly(DTE carbonate) and the fast degrading co-polymer poly(DTE-co-20%DT carbonate). Ultrafine fibers of these polymers were successfully fabricated using an electrospinning process. The effects of some solution and process parameters (i.e., polymer concentration, electrostatic field strength and solvent system) on morphological appearance and diameters of the obtained fibers were investigated by scanning electron microscopy (SEM). Smooth fibers were obtained at high enough solution concentrations (i.e., 15 and 20% (w/v)). The average fiber diameter was found to increase with increasing polymer concentration and applied electrostatic field strength. The electrospinnability of poly(DTE-co-20%DT carbonate) in dichloromethane was enhanced when methanol was used as the co-solvent. In all of the conditions investigated, the average diameter of the obtained smooth fibers ranged between 1.9 and 5.8 μm. A qualitative assessment of an as-spun mat of poly(DTE carbonate) fibers as a tissue scaffolding material showed that three different cultured cell lines appeared to adhere and propagate well within the scaffold. For poly(DTE carbonate) exceptionally high cell densities could be achieved after 10 days of cell culture.