Similiar to Jonas Appelgran's answer, but some slight changes to solve our issue.
- Download and install install Microsoft OLE DB Driver for SQL Server (MSOLEDBSQL)
- Replace Provider=SQLOLEDB; with Provider=MSOLEDBSQL19; in all connection strings for the ASP Classic scripts (note the version of the driver was needed)
- At this point, was still getting the following error:
SSL Provider: The certificate chain was issued by an authority that is
not trusted.
After some research, I found that I also needed to either trust the server certificate or set the encryption to false in the connection string:
Trust Server Certificate=True;
and/or
Use Encryption for Data=False;
Need to update these depending on your situation but it was an internal intranet application only for us so either option was fine. (Otherwise you would need to create and install either a self-signed certificate or one from your organization's CA.)