Would the cost of a taxi from Museu Calouste Gulbenkian to the airport cost more than taking the metro? Does anyone know the line I would take if I chose the metro?
I always take the metro. It costs much less and as long as I don't have a lot of luggage, I think it's easy to navigate and there is a nice map on the Metro site.
If you enter at the Praca da Espanha station on the blue line (close to the Museu), you will go one stop to S. Sabastiao and change to the red line. The red line will take you all the way to the Airport - the final stop.
Here is a link to the journey planner on the Metro site although it is slow: http://metro.transporteslisboa.pt/eng/customer-info/diagrams-and-maps/journey-planner/