Osteoarthritis and hypertension are comorbidities that may have a complex and bidirectional relationship that involves both systemic and local factors. Both diseases require long-term pharmacotherapy management by concurrent administration of antihypertensive and anti-inflammatory medications. Recently, a fixed-dose formulation containing both amlodipine (AML), as the besylate, and celecoxib (CXB) emerged to manage this comorbidity. This combination medicine is sold under the brand name Consensi® and is used in adults who have both osteoarthritis and high blood pressure. This systematic review gathers and discusses a variety of analytical techniques employed in the literature to quantify AML and CXB in their fixed-dose pharmaceutical formulation and other matrices, including capillary electrophoresis, UV-visible spectroscopy, spectrofluorimetry, electrochemical methods, and other chromatographic techniques such as LC-MS, UPLC, and GC. The comparative use of various analytical methods for quantifying CXB and AML is discussed in this review. Further analytical research for estimating CXB and AML may be successfully conducted using the information presented in this review paper.