Polymers are increasingly being used in higher demanding applications due to their ability to tailor the properties of structures while allowing for a weight and cost reduction. Solvents play an important role in the manufacture of polymeric structures since they allow for a reduction in the polymer’s viscosity or assist with the dispersion of fillers into the polymer matrix. However, the incorrect removal of the solvent affects both the physical and chemical properties of polymeric materials. The presence of residual solvent can also negatively affect the curing kinetics and the final quality of polymers. Destructive testing is mainly performed to characterize the properties of these materials. However, this type of testing involves using lab-type equipment that cannot be taken in-field to perform in situ testing and requires a specific sample preparation. Here, a method is presented to non-destructively evaluate the curing process and final viscoelastic properties of polymeric materials using ultrasonics. In this study, changes in longitudinal sound speed were detected during the curing of an aerospace epoxy adhesive as a result of variations in polymer chemistry. To simulate the presence of residual solvent, samples containing different weight percentages of isopropyl alcohol were manufactured and tested using ultrasonics. Thermogravimetric analysis was used to show changes in the decomposition of the adhesive due to the presence of IPA within the polymer structure. Adding 2, 4, and 6 wt.% of IPA decreased the adhesive’s lap shear strength by 40, 58, and 71%, respectively. Ultrasonics were used to show how the solvent influenced the curing process and the final sound speed of the adhesive. Young’s modulus and Poisson’s ratio were determined using both the longitudinal and shear sound speeds of the adhesive. Using ultrasonics has the potential to non-invasively characterize the quality of polymers in both an in-field and manufacturing settings, ensuring their reliability during use in demanding applications.