There are several study abroad programs which classics majors are encouraged to consider.
In Italy, committed students can enroll in a semester at the Intercollegiate Center for Classical Studies in Rome, a Duke University program open to students from any of the participating colleges (of which Beloit is one). The semester in Rome allows students to spend an intensive semester studying Latin or Greek with other American students and faculty and to supplement this study by visiting the physical remains of Roman culture in sites all over Italy.
Programs in Greece include The College Year in Athens and The Arcadia Center for Hellenic, Mediterranean, and Balkan Studies, both centered in Athens. Each of these two programs possesses unique opportunities for students (College Year in Athens is more focused on archaeology, art history, and general studies, while Arcadia Center offers opportunities more custom-tailored to a student's particular interests).
There are also other programs around the world that allow students to continue their study of ancient languages in another country (and even taught in a non-English language!), and programs that allow students to complete other Classics major requirements and can include ancient site visits (in, e.g., Spain, the U.K., France, Romania, Germany).
Learn more about these and other opportunities to study abroad on the Office of International Education's programs by majors page for classics.