Systems and methods for noncontact ablation of tissues or materials in/on the body using a luminal catheter and a catheter inserted into the lumen. In one embodiment, the luminal catheter is an ablation catheter and the other catheter is a recording/measurement/positioning catheter. The luminal catheter incorporates a noncontact ablation element such as an ultrasonic transducer. The luminal catheter can be inserted through the skin and into the body (e.g., into the heart) and the recording/measurement/positioning catheter can be inserted into the lumen so that the ablation and recording/measurement/positioning catheters are simultaneously positioned to record/measure the electrical activity of the target tissue and ablate the target tissue without causing the trauma that results from the introduction of additional catheters. Either of the ablation and recording/measurement/positioning catheters can be steerable, and either may incorporate recording/measurement electrodes.