From Lisbon (LIS):

Train: Get the metro at the airport (red line) to the railway station ORIENTE. From there, catch a train to Coimbra-B (trip duration of about 2 hours).

Train timetables and prices can be checked and booked at https://www.cp.pt/passageiros/en/train-times. Note that tickets can also be bought on-site at the railway stations (although for a higher price than if booked online in advance).
The “Alfa Pendular (AP)” and “Intercidades (IC)” are the fastest trains and the best option to travel to Coimbra.

Once in Coimbra-B station, you can connect directly to “Coimbra/Coimbra-A”, in the city centre (5 min ride, connection included in the “Alfa” or “Intercidades” fare) or, alternatively, ccatch city buses to the city centre (~20-25 minutes), or a taxi (10-15 minute ride). Coimbra city buses schedules and routes: SMTUC website (https://www.smtuc.pt/) or, alternatively, via the Moovit app (on this webpage, or using the Android app and setting the location to Coimbra).

Bus: There are several bus stops in Lisbon: at the airport, at the main bus stations (TERMINAL RODOVIÁRIO SETE RIOS), and at the ORIENTE train stations. Please consult corresponding websites to see the locations.

From Porto (OPO):

Train: Get the metro right at the airport, following the indications at the arrivals terminal (circular logo with an “M” inside). The entrance to the metro is right after the entrances to the parking lot. The easiest way path towards the city’s main railway station (CAMPANHÃ) is by taking metro line E (violet line) in direction of “Estádio do Dragão/Stadium”. You should leave at “CAMPANHÔ, that is, just one stop before “Estádio do Dragão”. Keep in mind that during part of the day, some metros (typically 1 in 2) will only go as far as the city centre (stop “Trindade”). In that case, leave at “Trindade” and wait for the next train towards “Estádio do Dragão” (there are several options). Total trip time should be below 40 minutes.

You can of course use standard trip planning apps, but keep in mind that some (e.g. google maps) will often propose complex combinations of bus and metro lines to get from the airport to the train station. The metro’s own journey planner (https://en.metrodoporto.pt/pages/391) will show you all metro routes with updated schedules (although no connections to other means of transportation). The Moovit app (with location set to Porto) provides full real-time public transportation info and routing.

From the Campanhã train station, catch a train to railway station Coimbra-B (trip duration of about 1 hour).

Train timetables and prices can be checked and booked at https://www.cp.pt/passageiros/en/train-times. Note that tickets can also be bought on-site at the railway stations (although for a higher price than if booked online in advance).

Once in Coimbra-B station, you can connect directly to “Coimbra/Coimbra-A”, in the city centre (5 min ride, connection included in the “Alfa” or “Intercidades” fare) or, alternatively, catch city buses to the city centre (~20-25 minutes), or a taxi (10-15 minute ride). Coimbra city buses schedules and routes: SMTUC website (https://www.smtuc.pt/) or, alternatively, via the Moovit app (on this webpage, or using the Android app and setting the location to Coimbra).

Bus: There are two main bus stops in Porto: at the airport, and at the CAMPANHÃ train stations. Please consult corresponding websites to see the locations.