This is further to my previous message, where I mentioned about exams of राष्ट्रिय-संस्कृत-संस्थानम्. In this message I would like to appraise you about exams of भारतीय विद्या भवन.
भारतीय विद्या भवन is certainly one of the oldest, maybe, the oldest institute offering exams in Sanskrit. Your basic question was about BA in Sanskrit. The कोविद exam of भारतीय विद्या भवन is said to be equivalent to BA in Sanskrit. In an old brochure the कोविद exam is called as पदवीपरीक्षा.
I would highly commend the exams of भारतीय विद्या भवन, because the textbooks themselves offer the best "graded" learning of Sanskrit, the best among, whatever exam and textbook schemes I have come across. The scheme of examinations is in steps as बालबोध (1 paper of 50 marks), प्रारम्भिक (1 paper of 50 marks), प्रवेश (2 papers of 50 marks each), परिचय (3 papers of 50 marks each) and कोविद (4 papers of 50 marks each). I hope, I am correct. You may please check at a center of भारतीय विद्या भवन nearest to you. Details of all centers of भारतीय विद्या भवन are available at their website
http://www.bhavans.info/kendra/index.asp
Textbooks of भारतीय विद्या भवन are fairly low-priced and are available in different languages. One can take the exam also in the language of one's choice. Language is important for two types of questions, (1) Translate the following from ___ language into Sanskrit (2) Translate the following from Sanskrit into ___ language.
The textbooks are called संस्कृत सरल शिक्षक. So, they are "Teach Yourself" books. But it would always be good, if you can find a teacher, because a good teacher will give some "insight", which will enhance the depth of understanding.
The exams are held twice in a year and the declaration of results and issuance of certificates is also quite well-organized.