Yes. It is mandatory to have a health insurance when you apply for your visa.
If you want to get Portuguese insurance you can contact an insurance company. The prices may vary from 150€ to 1000€/year depending on the company and what it covers.
Another option is to use social security. The social security insurance entitles you to free medical treatment and appointments in public hospitals and clinics, although dental treatment are not provided in the public health system. You can sign up for this after you arrive in Portugal. Please remember that for visa purposes you need show proof of alternative insurance (e.g from Carnegie Mellon). In case of Carnegie Mellon insurance, you can cancel it from the date you depart the US and receive a partial reimbursement.
Here is a list of private insurance companies you can contact:
Axa - http://www.axa.com/en/
Generali - http://www.generali-gw.com/
Ocidental - https://www.ocidental.pt/
Tranquilidade - http://www.tranquilidade.pt/
Império Bonança - http://www.imperiobonanca.pt/pt/Pages/imperio-bonanca.aspx
Aon Studente insurance - www.aon.pt
Pacific Prime Insurance Brokers Ltd. - http://www.pacificprime.com/
Highmark - https://www.highmark.com/
HCC Medical Insurance Services - http://www.mnui.com/
HTH Worldwide - http://hthworldwide.net/