A calibration strategy tries to match target moments using a model’s parameters. We propose tests for determining whether this is possible. The tests use moments at random parameter draws to assess whether the target moments are similar to the computed ones (evidence of existence) or appear to be outliers (evidence of non-existence). Our experiments show the tests are effective at detecting both existence and non-existence in a non-linear model. Multiple calibration strategies can be quickly tested using just one set of simulated data. Applying our approach to indirect inference allows for the testing of many auxiliary model specifications simultaneously. Code is provided.