The increasing prevalence of antimicrobial-resistant (AMR) bacteria along with the limited development of antimicrobials warrant investigating novel antimicrobial modalities. Emerging inorganic engineered nanomaterials (ENMs), most notably silver nanoparticles (AgNPs), have demonstrated superior antimicrobial properties. However, AgNPs, particularly those of small size, could exert overt toxicity to mammalian cells. This study investigated whether combining AgNPs and conventional antimicrobials would produce a synergistic response and determined the optimal and safe minimum inhibitory concentration (MIC) range against several wild-type Gram-positive and -negative strains and three different clinical isolates of AMR Klebsiella pneumoniae. Furthermore, the cytotoxicity of the synergistic combinations was assessed in a human hepatocyte model. The results showed that the AgNPs (15–25 nm) were effective against Gram-negative bacteria (MIC of 16–128 µg/mL) but not Gram-positive strains (MIC of 256 µg/mL). Both wild-type and AMR K. pneumoniae had similar MIC values following exposure to AgNPs. Importantly, co-exposure to combinations of AgNPs and antimicrobial agents, including kanamycin, colistin, rifampicin, and vancomycin, displayed synergy against both wild-type and AMR K. pneumoniae isolates (except for vancomycin against AMR strain I). Notably, the tested combinations demonstrated no to minimal toxicity against hepatocytes. Altogether, this study indicates the potential of combining AgNPs with conventional antimicrobials to overcome AMR bacteria.