A popular option for those who wish to remain in Portugal when their student visa has expired is to make an application to convert their student visa to a visa that enables them to reside and work here.
You must have an offer of employment and make the application within 30 days of the expiry of the term of your student visa. Once the work visa has been approved, you may apply for a residency visa.
An interesting alternative, for those who have completed a high level of studies (Masters/PHD level) would be to apply for a one-year visa to search for employment.
You will need medical insurance and proof of your ability to support yourself economically for the duration of the visa.
While you are not permitted to work with this type of visa, upon finding suitable work, you may convert the visa to a residency and work visa (as mentioned above).