To see an overview of citations in a particular university, you can perform an Address or Organization enhanced search in the Web of Science Core Collection. Select Core Collection at the top left of the Web of Science screen and type the name of an institution into the search box and click on the Address field by using the down arrow and click Search.
You should see a list of results and on the right hand side of the screen if there are less than 10,000 you can select Citation Report and this will give you an overview of citations of publications where the author(s) has/ have an affiliation to the chosen university. If there are more than 10,000 records, you will have to reduce the number for example by selecting a particular subject area or date range on the left of the screen. You can then import the records to Excel for example.
You can search for an institution such as a university using Scopus.
On the Scopus search screen, select Affiliation from the drop down menu next to the search box and type in an institution such as City, University of London and click search.
If there is more than one entry, click on the appropriate link and then you should see an Affiliation overview for the institution of documents, subject areas, authors etc. Click on the link next to Documents to see a list of documents authored by university staff.