Are there tools to implement an institutional open access policy? Many universities have adopted open access policies, giving their employees an incentive to make their scholarly articles freely available online.

To enforce this policy, universities should ideally keep track of the research output of their employees, and remind them to upload their papers if they are not freely available yet.

This is a rather time-consuming task: I wonder whether there are tools to facilitate or automate this process.

Such tools could perform some of the following tasks:


Track the published papers and match their authors with the employees list (probably using some bibliometric platform like crossref.org)
Locate freely available versions of these papers
Run a repository where the papers can be uploaded (there are plenty of tools available for this task)
Manage waiver requests from researchers who want to opt out of the policy
Provide statistics about the publication practices within the institution
Building on Cape Code answer, what you seek for is an institutional repository. There are many, but it depends by the single institution. You should ask yours. 

Software used are often DSpace and Eprints (but there are others): these systems let users upload pre-prints and other documents; release them with Creative Commons licenses, use DOIs (sometime provided by the very same institutional repository); provide digital preservation, provide statistics, etc. 

The open access movement has a strong component in librarians, who in the last decades built protocols and best practices. 

Every institution is different and offers different services.