Miniaturized test methods were developed and applied to measure the hoop strength of small tubular components. A diametrical loading method and an internal pressurization method using elastomeric insert were adopted in the development of testing methods. Detailed analyses to assess these testing methods were attempted by using theoretical solutions and finite element analysis for stress distributions and the characteristics of the Weibull statistics. To demonstrate the applicability of the test methods, commercially available alumina tubes and miniature silicon carbide coatings from surrogate nuclear fuel particles were tested and their fracture strength distributions were analyzed with Weibull statistics. The size scaling relationship on the fracture strength was investigated by correlating with effective surface area. Furthermore, the applicability of the testing methods was discussed in terms of multiaxial stress fields, altered stress distribution by flattened loading contact, and availability of insert, focusing on high-temperature applications.