A transseptal access stability system (TASS) and method of use thereof is disclosed. The TASS includes a venous sheath for reducing the likelihood of complications that may arise when performing transseptal punctures. The TASS uses either suction force or cryo-based energy for securing the fossa ovale against the rim of the orifice of the venous sheath. A method of performing a transseptal puncture using the presently disclosed TASS also is disclosed.