Background/Objectives: Increasing drugs’ stability and adequately protecting them against degradation will ensure a decrease in their price and broader availability of pharmaceutical substances. This is of great importance, especially for drugs used to treat the most common diseases in the population, such as hypertension. The study examined two newly synthesized substances from the angiotensin I-converting enzyme inhibitor (ACEI) group as potential drugs. ACEIs are among the leading drugs used in the treatment of hypertension in the world. The chemical modifications of the tested substances applied concerned the places most susceptible to degradation. The presented work analyzed the compatibility of new derivatives with selected excipients used in pharmacy. Methods: Thermogravimetric (TGA) and differential thermal analyses (c-DTA) were used as the main methods. In addition, non-thermal methods such as colorimetry analysis, Fourier-transform infrared (FTIR) and UV spectroscopy were used. Results: Based on the conducted studies, it can be concluded that the incompatibility of IND-1 with glucose anhydrous and lactose monohydrate occurs only when the mixture is stored at higher temperatures. For the remaining IND-1 and IND-2 mixtures with excipients, compatibility was demonstrated. Conclusions: The obtained results confirmed the usefulness of the applied thermal analyses (TGA and c-DTA) for assessing the compatibility of the tested potential drugs with excipients. However, in the case of incompatibility reactions of substances occurring under the influence of elevated temperatures, such as the Maillard reaction, it is necessary to use non-thermal methods to obtain the right result.