There are panniers and pannier/backpacks with laptop/tablet compartments. YEARS ago, before such existed, I bought a generic Targus over-the-shoulder laptop bag at the thrift store. I also had an old '80s CyclePro pannier with totally shot nylon, but perfectly good hardware, including a stiff steel plate. So I incorporated that hardware into the Targus bag. If it's just a laptop I'm carrying, it still works great. Basically a cheapskate version of what @MMACH 5 did.

My commute almost always also includes a bottle of drinking water and a lunch. And most recently, I've been issued a tablet for telecommuting. My most recent kit is a Topeak beam rack with the bolt-on vertical sides, and Topeak rack-top bag with the side compartments that open downward and sit against the vertical sides of the rack. Then I got a cheapo Amazon tablet sleeve as an "insert". Tablet goes into the sleeve in the side compartment, Lunch and water go in the rack-top compartment.

Duhh, pic!

A small laptop should fit such; a big 15-incher, not so much.