Carbapenem-resistant Gram-negative bacterial infections are a major public health threat due to the limited therapeutic options available. The introduction of the new β-lactam/β-lactamase inhibitors (BL/BLIs) has, however, altered the treatment options for such pathogens. Thus, four new BL/BLI combinations—namely, ceftazidime/avibactam, meropenem/vaborbactam, imipenem/relebactam, and ceftolozane/tazobactam—have been approved for infections attributed to carbapenem-resistant Enterobacterales species and Pseudomonas aeruginosa. Nevertheless, although these antimicrobials are increasingly being used in place of other drugs such as polymyxins, their optimal clinical use is still challenging. Furthermore, there is evidence that resistance to these agents might be increasing, so urgent measures should be taken to ensure their continued effectiveness. Therefore, clinical laboratories play an important role in the judicious use of these new antimicrobial combinations by detecting and characterizing carbapenem resistance, resolving the presence and type of carbapenemase production, and accurately determining the minimum inhibitor concentrations (MICs) for BL/BLIs. These three targets must be met to ensure optimal BL/BLIs use and prevent unnecessary exposure that could lead to the development of resistance. At the same time, laboratories must ensure that results are interpreted in a timely manner to avoid delays in appropriate treatment that might be detrimental to patient safety. Thus, we herein present an overview of the indications and current applications of the new antimicrobial combinations and explore the diagnostic limitations regarding both carbapenem resistance detection and the interpretation of MIC results. Moreover, we suggest the use of alternative narrower-spectrum antibiotics based on susceptibility testing and present data regarding the effect of synergies between BL/BLIs and other antimicrobials. Finally, in order to address the absence of a standardized approach to using the novel BL/BLIs, we propose a diagnostic and therapeutic algorithm, which can be modified based on local epidemiological criteria. This framework could also be expanded to incorporate other new antimicrobials, such as cefiderocol, or currently unavailable BL/BLIs such as aztreonam/avibactam and cefepime/taniborbactam.