Florence offers many different concerts all year round.
The Maggio Musicale Fiorentino is certainly the most famous festival. The finest artists (conductors, soloists, singers and orchestras) from all round the world have performed at Teatro Comunale during the festival. From the 20th to the 30th of March, there will be several violin and opera concerts. I recommend you check out at the Maggio Musicale Fiorentino calendar.
At the recently opened Auditorium al Duomo on March 20th and 27th you'll be able to see La Traviata by Giuseppe Verdi. It is located near Piazza Duomo in Florence's city center.
In the Church of Santa Maria de' Ricci in Via del Corso, there is a concert almost every night. They generally play classical music such as Bach, Vivaldi, Purcel or opera and organ concerts. There isn't an official calendar since they show their program weekly. I suggest you go directly to the church and ask for information.
At St Mark's Church in via Maggio you can enjoy both opera and classical concerts. In March there will be La Bohème, Carmen and La Traviata. Here is the calendar for St Mark's Church.
On Sunday March 21st at 3 p.m. at the Odeon Theater near Piazza Strozzi La Bohème by Giacomo Puccini will be performed by the Royal Ballet from the Royal Opera House of Covent Garden in London.
In the Church of Santo Stefano al Ponte Vecchio from March 27th to April 2nd the Festival of World Sacred Music Week will take place, where young talents from around the world will play.
When you arrive in Florence, I recommend you go to the Tourist Information Office (near Duomo or near Train Station) and ask for a Florence events calendar which is updated weekly.
I hope my suggestions answered your questions. Don't hesitate to come back.
Your advise was most excellent. While searching the Teatro Comunale we found that our favorite italian singer, Paolo Conte will be performing and we were able to get tickets.
We saw him 5 years ago at the Chicago Symphony Center and were moved by the artist. the audience was very European, all dressed chic in basic black.