Most shrubs will try to grow back from their roots. Depending on the species and how well established the root system is, they may put up more or less of a fight. Typically you will need to do more than just cut them down in order to completely kill them.
You can kill most of the roots by painting concentrated glyphosate-based herbicide directly on the cut surface of the stump, immediately after cutting it. A paintbrush will work for this, or a sponge, or you can put the herbicide in one of of those bottles with a sponge dauber on the end (they're used for playing bingo and arts-and-craft projects, so a store that sells craft supplies should have them). Be sure to wear waterproof gloves. It's important to get the herbicide on the stump within 10 minutes after cutting, because the cut surface will immediately start drying out and quickly lose its ability to absorb the herbicide. Note that any ready-to-use herbicide that comes in a spray bottle will not have a high enough concentration; you want the concentrated stuff that has to be diluted before it can be applied as a foliar spray. Ideally it will be about 20-30% glyphosate, but as long as it's at least 10% it should work. Or if you can get ahold of a triclopyr-based herbicide at similar concentrations, you can use that instead of glyphosate. Wait a few weeks before installing your planter to make sure the shrubs are thoroughly dead.
If you don't want to buy a whole bottle of concentrated herbicide just to kill two shrubs, you can cut them down and see how much they grow back. Some species will only put
up a weak fight, and you may be able to sap its energy and eventually kill off the roots by repeatedly cutting any new growth. Or you can wait until the leaves on the new growth are fully expanded, then spray them with regular-strength herbicide (the kind that comes ready-to-use in a spray bottle). Various kinds of herbicide will work for this, but make sure the kind you buy is systemic (kills the roots, not just the leaves) and either non-selective (kills all kinds of plants) or selective to broadleaf plants. Keep an eye on the ground around the stump, up to several feet away, for new growth. Some species can regrow from the ends of roots as well as from the main stump.
If you have a weak and sickly shrub, you might get away with just cutting it down and installing a planter on top of it. But the risk is that if it does grow back, the new growth will damage your new planter. So the safest course is to make sure the shrubs are completely dead before installing the planter. If your planter is something you're willing to risk having damaged, or if it would be easy to move in order to attack the re-growing shrub, then go ahead and try cutting them down and putting the planter on top.
Don't bother with salt unless you want to poison your soil so nothing will grow there again (you've heard the expression, "salting the earth," right?). It's not an effective way of killing specific plants. If you add enough salt to kill these shrubs, it will contaminate the soil and kill the surrounding lawn and plants. People who talk about using salt as a substitute for herbicides are kidding themselves. If you don't want to use herbicides, don't use herbicides. But salt is not a substitute.