How can I fix a wobbly antique end table?

It depends on what you mean by 'wobbly', Marie. If the leg joints are loose, they will need to be glued, then strapped or clamped until the glue dries. Here's a link with more information:

https://homeguides.sfgate.com/reglue-table-leg-32957.html

Hi Marie, sometimes all legs need is for their screws to be tightened up. You can also consider adding L brackets on the inside for extra support. If its a foot issue you can add felt pads to the feet.

here is some info for you

https://www.youtube.com/watch?v=Wrr83QShcEk

You can reinforce and stabilize it by adding braces across the bottom. You can do this in an "X" pattern or box in all 4 legs. If you box in the 4 legs, you can also add a piece of plywood there for a second platform area.

Are the legs uneven? Sometimes there is a tiny discrepancy and all you need is a small felt pad on one of them.

check to make sure there are not any screws that can be tightened. If glue was used to adhere parts, check to see if they are fully stuck together. If not, get some wood glue. Then check the flooring. Is it on an easy surface? If not, get some wood shims to place under the feet and then it won't wobble.

Hello. I have repaired wobbly joints with superglue and fine sand placed in the underside joints. It might be something to consider.

https://www.saxtonblades.co.uk/blog/how-to-fix-wobbly-table-4-easy-steps/#:~:text=If%20your%20table%20legs%20are,to%20get%20the%20legs%20steady.

Joints might need wood glue

Check all your joints to see if they are loose. Check all your bolts and/or screws underneath and see if any have worked their way loose. Tighten as needed. May need to use fasteners to stabilize and/or wood glue.

Use a good grade of wood glue. If it has screws that have worn away the wood and won’t tighten, I suggest using a couple of bits of wooden toothpicks and put them into the hole and then put the screw into the hole and tighten the screw. I know it sounds crazy but it really works. I just tightened a couple of screws yesterday on an antique ladies writing desk.

it maybe your floor issue not table .. I would just change its location or add padding to leg

Hello. I have rescued some three dollar chairs that were very wobbly by using superglue and a little bit of powder or sand into the dowel cracks of the chair legs. The same thing could be done with a little baking soda and super glue. It’s stiffens up the wobbly joints.