A comparison is made of the three numerical techniques for evaluating the vector potential arising in the problem of a vertical current element radiating over a lossy ground: (i) the exact Sommerfeld integration, (ii) the high-contrast approximation (HCA) and (iii) the reflection-coefficient method (RCM). Extensive calculations are carried out to determine the range of applicability of the approximate techniques. The comparison shows good accuracy of the results derived from HCA for a relatively wide range of parameters of practical interest and indicates that the RCM is of a questionable validity for the vertical-antenna problem.