A novel catheter-based system that ligates the left atrial appendage (LAA) on the outside of the heart, preferably using a combination of catheters and/or instruments, e.g., a guide catheter inserted into the interior of the left atrial appendage that may assist in locating the left atrial appendage and/or assist in the optimal placement of a ligature or constricting element on the outside of the appendage, and a ligating catheter and/or instrument outside the heart in the pericardial space to set the ligature or constricting element at the neck of the left atrial appendage.