Aim To describe the occurrence of carbapenem resistance among multidrug-resistant (MDR) Escherichia coli and Klebsiella pneumoniae isolated from clinical specimens in Accra using phenotypic and genotypic methods. Methodology The study was cross-sectional, involving 144 clinical MDR E. coli and K. pneumoniae isolates recovered from the Central Laboratory of the Korle Bu Teaching Hospital (KBTH). The isolates were re-cultured bacteriologically, identified using standard biochemical tests, and subjected to antibiotic susceptibility testing using the Kirby-Bauer method. Carbapenem resistance was determined based on imipenem, meropenem, and ertapenem zones of inhibition, as well as minimum inhibitory concentrations (MICs). Carbapenemase production was determined phenotypically by modified Hodge test (MHT) and modified carbapenem inactivation method (mCIM), and genotypically with multiplex PCR targeting the blaKPC, blaIMP, blaNDM, blaVIM, and blaOXA-48 genes. Results Of the 144 MDR isolates, 69.4% were E. coli, and 30.6% were K. pneumoniae. The distribution of antimicrobial resistance rates among them was ampicillin (97.2%), cefuroxime (93.1%), sulfamethoxazole-trimethoprim (86.8%), tetracycline (85.4%), cefotaxime and cefpodoxime (77.1% each), amoxicillin-clavulanate (75%), ceftriaxone (73.6%), ciprofloxacin (70.8%), levofloxacin (66.0%), cefepime (65.3%), ceftazidime (64.6%), gentamicin (48.6), piperacillin-tazobactam (40.3%), cefoxitin (14.6%), amikacin (13.9%), ertapenem and meropenem (5.6% each), and imipenem (2.8%). In total, 5.6% (8/144) of them were carbapenem-resistant (carbapenem MIC range = 0.094–32.0 μg/ml), with 75% (6/8) of these testing positive by the phenotypic tests and 62.5% (5/8) by the genotypic test (of which 80% [4/5] carried blaOXA-48 and 20% (1/5) blaNDM). The blaVIM, blaIMP, and blaKPC genes were not detected. Conclusion Although the rates of antibiotic resistance among the isolates were high, the prevalence of carbapenemase producers was low. The finding of blaOXA-48 and blaNDM warrants upscaling of antimicrobial resistance surveillance programmes and fortification of infection prevention and control programmes in the country.