While I'd agree that relative and absolute are opposites, I don't feel that these two sentences are opposite in meaning, just a varying degree of 'high cost'. The first is kind of high, a bit high, high when compared to similar projects. The second is extremely high, whether for this kind of project or something else, it's a very large cost.
I'd say that a sentence expressing the opposite of the entire meaning would include the word 'low'.
"The cost of the project was considered relatively low" I feel is opposite in meaning to the first sentence.
(not a teacher, just a language lover)
Student or Learner