TERA Foundation has proposed and designed hadrontherapy facilities based on novel linacs, i.e. high gradient linacs which accelerate either protons or light ions. The overall length of the linac, and therefore its cost, is almost inversely proportional to the average accelerating gradient. With the scope of studying the limiting factors for high gradient operation and to optimize the linac design, TERA, in collaboration with the CLIC Structure Development Group, has conducted a series of high gradient experiments. The main goals were to study the high gradient behavior and to evaluate the maximum gradient reached in 3 and 5.7 GHz structures to direct the design of medical accelerators based on high gradient linacs. This paper summarizes the results of the high power tests of 3.0 and 5.7 GHz single-cell cavities.