Generally Xではある is an emphasis by contrast with non-Xである(or Xでない). More verbosely it means if I were to describe it X or non-X, I would say X.
I think it is similar in English when the verb is pronounced emphatically. E.g.,
- It is feeble but some warmth was felt. (with emphasis on is)
Here at least in some sense, is should be contrasted with is not.
The difference of かすかではあるものの and かすかであるものの in the question is as subtle as that of the above and the version without emphasis on is (It is feeble but..).
Practically, Xではある indicates that there is a reservation or more simply it translates X, but... Like the sentences in question, if the "but ..." part is not omitted, it does not make a lot of difference.
When nothing follows after ではある, then it makes a difference. For example,
- この映画は人気だ(人気である)
- この映画は人気ではある
The former is a plain statement that the film is popular. The latter indicates there is "but". The implication may be that the speaker does not like it or that the film cost too much money and hence is commercially not that successful. It depends on context.