It's fair to say that UB will not be a part of the NCAA or NIT tournaments. But both the CIT and CBI tournaments are in play.
The CollegeInsider.com Postseason Tournament (CIT) was created in 2009 by Collegeinsider.com. In 2012 it expanded to 32 participating teams. The Tournament is oriented toward mid-major schools who did not get selected to go the NCAA or NIT tournaments.
The tournament consists of five rounds, single elimination-style, and claims to "use the old NIT model in which matchups in future rounds are determined by the results of the previous round". Criteria for selection include, but are not limited to win-loss record, strength of schedule, strength of conference, and final ten games. Participating teams must finish the regular season with a .500 winning percentage or better to qualify, with the exception of the Great West Conference Tournament winner, who was given an automatic bid to play in the CIT if they are not given an at-large bid to participate in the NCAA or NIT tournaments. In 2013, The Chicago State Cougars won the Great West Conference Tournament, thus becoming the first team to participate in the CIT with a sub-.500 record (11–21).
The College Basketball Invitational (CBI) tournament was created in 2007 by The Gazelle Group. The CBI selects 16 teams that are not selected for the NCAA Tournament or the National Invitation Tournament (NIT). From 2008 through 2010, teams competed on the home court of the higher-seeded team. Seeding was not included in the 2011 tournament and teams had to pay to play home games prior to the finals. The tournament is single elimination, until the final two teams are determined, and then the championship is determined by a best two-out-of-three format.