I have a RESTFul API that I want to secure using SSL Certs. If I were to get some SSL certificates, would I need separate ones for each of my web clients that use my API or
SSL Certificates are for Web Server. You install them in your Web Server. Certificates are matched to your domain. They have nothing to do with the clients. Any client can access your server if you have a valid certificate.
I think you have multiple Resful API's. Now you need not have separate Certificates for API's since Certificates are matched to your server's domain and not to the API's you host. You can have any number of API's and Clients connected to your server using a SSL Certifcate.