Ian,

Some software I use (e.g. Autocad) uses software licensing which works over the web and allows me to install on as many computers as I like, but permits me to run only one instance of the application at any one time. ... Some other software I use also provides for this form of licensing, but the vendors charge a disproportionately large premium for the privilege (I’m not sure whether Mathematica offers this option)

Wolfram offers a Network License that works this way. You install a "license server" on your network -- any machine that is always on will do-- and you "check out" the license on any machine.

If you have an unusual licensing situation (like you describe), I have found Wolfram to be very accommodating. You should contact your sales representative. They have helped me in the past on multiple occasions.

Regards,

Neil

Thank you for your reply. I purchased the Mathematica Student Edition(Personal License Service). I used my license in the first computer. and then I tried to use it in the Second computer.
But, I saw below picture. What is the problem?

Each activation key only works on one machine. If you have questions about the capabilities of your specific license I'd email customer support using this form: http://www.wolfram.com/support/contact/email/

This is because the license is not the same thing as the activation code. You'll need a different activation code for your second installation. Contact Wolfram Support at http://www.wolfram.com/support/contact/email/ and they'll sort it out for you.