There is an argument that the only type of assessments that are objective are tests. This statement is not necessarily true. There are so many different ways to evaluate a student's learning. Many assessments can give much more insight to what a student has gained than the traditional test.
Several examples of alternative assessments are projects, ongoing journals, blog posts, electronic portfolios, participation in simulations and labs, discussions, integrated response systems (CBLs), and teacher observation. It is sometimes more difficult to evaluate these forms of assessment in an objective way, but that is when rubrics come in handy. A rubric has stated objectives with varied levels of mastery so that it is very clear what is being evaluated. When a teacher is specific in what they are looking for in a student's learning it becomes possible to use a multitude of assessments and still grade objectively.