Tons. It may not be actual shield pressure, but I will try to go into a little depth.
Slow:
Slow stuff won't work against a fast opponent, or an opponent who knows mario well.
Bair waveland (spaced) either side of the shield, and waveland through the shield. Once you are good at this you will find with a perfect waveland, mario can cancel the momentum of the waveland by jumping and doing an aerial. I like to bair waveland the front of the shield, waveland behind them but cancel that momentum with a SH uair as soon as I am behind them. This autocancels, so you can do alot of stuff afterwards. Jab jab -> dsmash, jab utilt.. anything. A nair will go through the shield on larger opponents after landing these 2 hits.
My favorite - you uair (autocancel always) through the shield, so you are now behind the opponent, and then bair waveland back infront of them. Now you do a tiny dash forwards and nair back through the shield with full forwards momentum. This will poke the shield.
Janky - wavedash, jab, utilt. If you space the utilt well, the opponent may try to grab you and miss. This allows you a free fsmash.
Medium:
Fair has enough shield stun and range to allow free late hits on the shield. Unfortunaly it's difficult to follow up - the options are jab, another spaced fair, or buffer a full hop and dair above them. You can follow this dair up with a late uair either infront or behind the shield, or bair or nair or whatever. Don't forget running away after hitting the shield is always an option. It's good to dash dance just outside of their SHFFL range, especially against marth.
Autocancel a bair/uair on their shield. Follow up with jab -> dsmash or something fancy like x2 jab -> fair -> buffer fullhop dair
Spacing a SH dair on the edge of the shield is a very good and underused mario technique. Often the floor hit will spike the shield. There is too much shield stun for the opponent to attack until the move has finished in it's entirety.
Full hops open some cool options to mario. By doing a rising uair on a shielding opponent, mario can fastfall back downwards and get a very late nair on the front of the shield, or a very late bair on the back of the shield.
Fast:
Fullhop fireball waveland -> jab/grab/dash -> pivot grab. This is sexy.. tough to get the hang of but extremely useful. Often the opponent will shield to block the fireball, and has no idea mario can waveland out of this fireball. Get the perfect waveland down, and you will find mario can easily get behind the opponent/infront and grab just as the fireball hits. This is legitimate shield pressure if it's timed properly.
This stuff isn't practical, but it exists as mario's other true shield pressure so I'll include it.
Mario can get 2 moves out in a short hop. These moves are bair + nair, and uair + nair.
Bair + nair can always come out, whereas uair -> nair only works on a shield. If you land both hits of either combo you are i a strong position to get some free hits and strong momentum, but in the long run you will most likely end up losing more stocks from trying this than you will actually take.
To conclude, mario doesn't have any free shield pressure, but he can space against all the shields and he has a **** ton of options. To use the options effectively you must be creative and have finesse with the plumber.. he has great attack speed and good aerial movement. An understanding of sliding, perfect wavelanding and how momentum works is essential to pull alot of this off.
Just switch to falco instead.