Wherever you decide to go to school, make sure you find out exactly what tests are required to get in.
There are specific admission tests that most schools require from applicants, like the Secondary School Admission Test (SSAT), or the Independent School Entrance Examination (ISEE). If you are an international student, you may also be asked to provide English proficiency test scores from the Test of English as a Foreign Language Junior (TOEFL Junior).
(UPDATE: The SLEP was discontinued in summer 2012).
Some schools will also accept the PSAT, the SAT 1, and the ACT.
Be sure to contact the admission office of the boarding schools you’re interested in to determine exactly which tests they require.