I implemented the Levenshtein algorithm in Java and am now getting the corrections made by the algorithm, a.k.a. the cost. This does help a little but not much since I want
The maximum value of the Levenshtein difference between two strings would be the maximum of the length of the two strings. (That corresponds to a change of symbol for each of the characters up to the length of the shorter string, plus inserts or deletes depending on whether you're going from shorter to longer or vice versa.) Given that, the similarity of the two strings must be the ratio between that maximum and the difference between that maximum and the actual Levenshtein difference.
Implementations of the Levenshtein algorithm tend to not record what those edits should be, but it shouldn't be that hard to calculate given the abstract algorithm on the Wikipedia page.