A transcatheter delivery device including a catheter and at least one stabilizer useful for transseptal procedures. The stabilizer includes a shaft connected to an anchor. The anchor has a delivery position in which the anchor is collapsed against the shaft and a deployed position in which the anchor expands to engage a pulmonary vein or atrial appendage to support the catheter within the septal wall as the catheter moves within a left atrium. Various disclosed delivery devices are also configured to ablate tissue proximate the anchor and/or can be disconnected from the delivery device after the procedure to occlude an atrial appendage. Methods of using the disclosed delivery devices and treating a heart are also disclosed.