Currently the Halal certified outlets are mainly fast food chains. There are also a number restaurants which assure that they serve Halal food, although they have no certfication. Most of them are Muslim owned. It is advisable to check with locals before you select such a restaurant to dine.
Apart from the fast food chains and the fine-dining restaurants, there a quite a number of roadside food outlets which are Muslim owned and serve "Halal Food". These outlets will generally have a Muslim name and have signage to refelect that. They are not upmarket restaurants, but some of them probably serve some of the best local cuisine in Sri Lanka.
Being a majority Buddhist country, there is also a wide selection of vegetarian food outlets all across the island.
The locals mainly have rice with vegetable and meat/fish curries. The local food is generally spicy, but some of the restaurants catering to the visitors to Sri Lanka, do serve milder versions of Sri Lankan Cuisine.
There are also a variety of snacks known locally as "Short eats". They are generally sold in bakeries or coffee shops. Most of them do not have a Halal certificate. Although most of them do not serve pork based "short eats", it is good to check with local Muslims where to buy Halal ones. They are great snacks to have as starters or with tea or coffee. They also have a range of sweets made from rice flour and coconut milk.
Halal Certfication is been done by ACJU. They are a non-political, non-governmental national religious institution in Sri Lanka exclusively for Muslim theologians. They are now a member of the World Halal Council. You can look for their logo at food outlets that are certified by them.
There are also now a range of food items that are also certfied by ACJU you could find in Supermarkets in Sri Lanka.