You could by a 1 inch tile hole saw as suggested, if this is porcelain tile which is the hardest damn substance to drill through I would skip the hole saw and get a small, cheap masonary bit like 1/16 for about $2.50, do just what you suspected, drill out small holes in a circle. If I used a hole saw and you did the multiple holes you would be done with both tiles before I even got 1/4 of the way through the first one, and by the time I got to the second one I would be working with a hole saw with half it's drilling power left.
Pros drill through porcelain tile with holes saws that are diamond coated and the bits cost upwards of $250 bucks each. You can do the job for $2.50.