Hi jonasg@embarqmail. Com. Welcome to the forum. The common things to look for are a bent wheel, broken belt in a tire, or worn front end parts. Normally you will feel the wheel and tire without having to slow down. Worn ball joints or tie rod ends can cause symptoms to change between the load of cruising and the drag of road force when coasting. Also, a sticking front brake caliper can cause a wobble but those too usually occur when cruising, not just when coasting.
The steering and suspension systems should be inspected by an alignment specialist. There are things you can do yourself too. Jack up the front tires off the ground and run the car in gear. Watch the outer edges of the wheels to see if they're moving left and right as they rotate, and watch the tread of each tire for humps or sideways squirming. Typically only one wheel will spin. If you hold it, (I like to use a 2x4 as a pry bar, but be careful it doesn't catch and become a projectile), the other wheel will start to spin.