Kristian O'Leary's testimonial lasted just 14 minutes after the stalwart was forced off with a virus.
But his team-mates did their best to make up for it, first Tom Butler forcing a good save from Dean Kiely from his right foot shot.
And then Darren Pratley missed from eight yards after good work from Febian Brandy before Guillem Bauza came close.
West Brom had a couple of chances themselves and the best chance fell to Paul Robinson who headed wide.
• Swansea manager Roberto Martinez: "It was a good test. Playing against a Premier League side from a tactical point of view, you've got to be spot on.
"I think after all the work we did in Spain, the boys did very well.
"We had to work really, really hard to maintain West Brom and keep a clean sheet."
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