Systems for engaging a bodily tissue and methods of using the same. In at least one embodiment of an exemplary system for use with a vacuum source for engaging a tissue of the present disclosure, the system comprises an engagement catheter comprising a proximal end, a distal end, first and second lumens extending between the proximal end and the distal end, and a skirt operatively connected to the distal end, an inducer sheath having a proximal portion, a distal portion, and a lumen extending therethrough, the inducer sheath configured so that it is capable of insertion into the second lumen of the engagement catheter, a dilator comprising a tapered tip at a distal end and a hollow channel extending therethrough, the dilator sized and shaped for insertion into the lumen of the inducer sheath, and a vacuum port located at the proximal end of the engagement catheter, the vacuum port being operatively connected to the first lumen of the engagement catheter and capable of operative connection to a vacuum source. In various embodiments, the systems further comprise an inflatable balloon at or near the distal portion of the inducer sheath.