Current Kosher options in Boston.
If you are looking for shabbos - if you can make it to Brookline - The Butcherie on Harvard Street has a full takeout counter. Not all their meat is GLATT (they sell both) - so depending on your kashrut needs, be sure to ask.
Other options for shabbos food that will deliver:
Rubin's Deli in brookline will deliver shabbos meals
Milk Street Cafe located downtown may provide shabbos food delivery through their corporate catering division. Their restaurant does not offer shabbos food to be purchased.
In terms of Saturday night and Sunday - all your kosher options are going to be in Brookline. Given that shabbos is over late, not sure what will be open - likely only Taam China.
Good options for Sunday include:
Cafe Eilat (pizza/dairy)
Taam China (chinese)
Rami's (middle eastern)
Jerusalem Grill (Israeli)
I've not been to Boston in a really long time, but check to see what the Butcherie might be able to do. According to their web site (www.butcherie.com, phone number is 617-731-9888) they have a variety of prepared foods. Maybe they do Shabbos specials, too - a lot of places like that tend to have some sort of special (soup, roast chicken, and kugel, usually), but I don't know if they would deliver.