There is a useful counterpart of conformal prediction for e-values, called conformal e-prediction. Conformal prediction can serve as basis for testing the assumption of exchangeability, leading to conformal testing. Similarly, conformal e-prediction can also serve as basis for testing. The resulting conformal e-testing looks very different from but inherits some strengths of conformal testing; it even has some advantages over conformal testing. In this paper we discuss systematically both strengths and limitations of conformal e-testing.