When generating a migration script there should be options to indicate if an object exists then, take the appropriate action (create/alter)
Basically when you compare then you want the script to generate by checking if the database object exists then perform the appropriate action. So, if you are updating a stored procedure then there should be two blocks of statements where the first block is to check if the stored procedure exists and if not exists then create the stored procedure else alter the stored procedure. This should be applied to other database objects such as tables, columns, views, functions, stored procedures, user defined table types, etc.
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Muhanned Maayeh commented
I was referring to SQL Source Control 4 as it generates a migration script.
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Are you referring to SQL Compare or SQL Source Control?