Antimicrobial resistance is a major threat to both individual and population health in the 21st century. Meropenem is a broad-spectrum β-lactam antibiotic of the carbapenem class with low toxicity. However, resistance to it has increased in Gram-negative bacteria, particularly due to the bacterial expression of β-lactamases. New Delhi metallo-β-lactamase (NDM-1) is one of the most recent additions to the β-lactamase family and is of growing concern as no approved inhibitor exists. This study aimed to identify an NDM-1 inhibitor that could be given as an adjuvant, thus re-establishing meropenem susceptibility in multi-drug resistant pathogens. In silico screening was conducted using the NDM-1 protein structures from Klebsiella pneumoniae and Escherichia coli. Structure-based and ligand-based drug design protocols were implemented by screening four small molecule databases. More than 720,000 compounds were initially screened, and extra precision docking was employed to help select compounds for antibacterial activity evaluation based on the highest binding affinity demonstrated by docking with NDM-1. All the selected compounds were predicted to bind more effectively than meropenem to NDM-1, reinforcing their potential to competitively inhibit the enzyme. The compounds with the best binding scores contain charged and polarised groups, leading to the formation of unique hydrogen bonds with NDM-1 residues and significant binding to the two zinc ions in the active site. In vitro broth microdilution testing was used to measure the biological effect of the test compounds by determining the minimal inhibitory concentration (MIC) and fractional inhibitory concentration index (FICI). The MIC for meropenem against E. coli ATCC BAA-2452 was 16 μg/mL, which was reduced by three-fold to ≤2 μg/mL when meropenem was used in combination with the bisphosphonates risedronate, alendronate and zoledronic acid at a concentration of 256 μg/mL. These results support the potential for the use of existing compounds as adjuvants to overcome meropenem resistance due to NDM-1.