Due to limited therapeutic options, combination therapy has been used empirically to treat carbapenem-resistant Acinetobacter baumannii (CRAB). Polymyxin-based combinations have been widely studied and used in the clinical setting. However, the use of polymyxins is often limited due to nephrotoxicity and neurotoxicity. This study aimed to evaluate the activity of non-polymyxin-based combinations relative to polymyxin-based combinations and to identify potential synergistic and bactericidal two-drug non-polymyxin-based combinations against CRAB. In vitro activity of 14 two-drug combinations against 50 A. baumannii isolates was evaluated using the checkerboard method. Subsequently, the two best-performing non-polymyxin-based combinations from the checkerboard assay were explored in static time-kill experiments. Concentrations of antibiotics corresponding to the fractional inhibitory concentrations (FIC) and the highest serum concentration achievable clinically were tested. The most synergistic combinations were fosfomycin/sulbactam (synergistic against 37/50 isolates; 74%), followed by meropenem/sulbactam (synergistic against 28/50 isolates; 56%). No antagonism was observed for any combination. Both fosfomycin/sulbactam and meropenem/sulbactam combinations exhibited bactericidal and synergistic activity against both isolates at the highest clinically achievable concentrations in the time-kill experiments. The meropenem/sulbactam combination displayed synergistic and bactericidal activity against one of two strains at concentrations equal to the FIC. Non-polymyxin-based combinations such as fosfomycin/sulbactam and meropenem/sulbactam may have a role in the treatment of CRAB. Further in vivo and clinical studies are required to scrutinise these activities further.