One option would be Peerage of science, http://peerageofscience.com/, which is a service through which you can request peer reviews (which are also reviewed) for your articles and review the articles of others. There are, however, two problems, one of them significant:
- The review criteria are not a good fit for mathematics articles. This is a minor issue, really, but annoying. See below for more details.
- To my knowledge, the service is not popular among mathematicians. This can be slowly changed by using the service, but there is no immediate solution. The service is free for scientists.
Quality indices at Peerage of science are: question, data, methods, inference, writing. Of these, data is not relevant for pure mathematics, and both methods and inference require interpretation.
The refereeing format is standardised and there is plenty of room for discussion, so one is in now way communicating only through the five indices.
Why it might become popular among mathematicians
The main users of Peerage are biologists (of certain subfields), but the benefits are common to all fields of science where one publishes articles: One can request a peer review and then, when submitting to a journal, tell that the article has already been peer reviewed, with a link to the review. The journal, of course, is free to do their own review, if that is what they would rather do. If the article is rejected, then one can send it to another journal and share the same review at Peerage.
This reduces the work load of referees and editors and speeds up the process for authors.
The peer reviews are reviewed, so their credibility is also measured.
The reviewers can get their work recognised. One can get credit as an excellent reviewer, for example.
There are further benefits with respect to some journals that are linked to the service, but I don't think this is relevant to mathematicians at this point.