With careful planning I found that I could reach both Cerveteri and Tarquinia by public transport on a day trip from Rome. I took a train to Cerveteri-Ladispoli which connected with a bus to Cerveteri town centre, from where I got a shuttle bus to the necropolis.
After a very satisfactory walk amongst the tombs I retraced my route to Cerveteri-Ladispoli station and caught a train to Tarquinia, changing at Civitavecchia on the way. At Tarquinia a CD bus took me to Piazza Cavour and then continued to the Necropolis.
After the visit I walked back down to Piazza Cavour to catch a bus to Tarquinia station and caught a train direct to Rome.