Be glad the nests are gone if they are truly House Sparrows. They are non native, invasive species and they kill our Native cavity nesting birds like Bluebirds, Chickadees etc.
Go to www.sialis.org to see if your birds are really House Sparrows...If they are...well I shoot them. Nuff said. If they aren't then the sialis site will also give you suggestions on how to protect your cavity nesters.

Thanks Lisa -- and I am sure they are house sparrows, but living in the middle of the city bluebirds aren't interested in our property. I was hoping the sparrows might eat some grubs, slugs, but perhaps they only eat seeds? I'm not planning to shoot them (the city frowns on that practice), but the neighbourhood cats do a pretty good job actually. I'll check out the site you suggested.
Jan

Yes I'm pretty sure they would frown on it in the city. I'm out here in the woods. When they brought the English House Sparrows over they thought they would eat bugs too. They are very damaging. There are other ways to get rid of them (also on the site)Don't let them multiply. Native cavity nesters Blues, Tree Swallows etc. eat lots of bugs but hey are not likely to take up residence where there is an over abundance of HOSPs.

I'm curious about the origial topic of the post... squirrel-proof birdhouses. I have had that same problem and would love to hear suggestions. (aside from shooting the squirrels)

Garden Guy the sialis.org website has plans & explains how to keep nestboxes safe.

The same way you keep the squirrels away from bird feeders. First you put the bird house on a pole because squirrels can climb down anything. Next, locate the pole 10 feet away from any trees and about 5 feet off the ground, then attach a squirrel baffle. Actually I recommend a raccoon baffle, which would be longer since raccoon are a greater danger than squirrels. If you get a metal one, it will probably stop snakes, too.

Paul