Hello guys! New to Olimar board though I've been playing him since brawl, and in PM since he was released. I have experience in the Falco matchup because my scene has many oldschool melee players who just use their spacies in PM.
Falco can be up-throw or down-throw chaingrabbed at low percents obviously. Your opponent can DI the throws so that they land behind you, and this can be a pain to deal with because Olimar's grab can whiff at point blank range. You can remedy this by simply doing pivot grabs. You want to land a grab or chaingrab into a blue pikmin grab, because blue up-throw has enough knockback to start a combo on fast fallers, even at 0%. Easiest and most reliable combo after up-throw is up-smash, (maybe 1 or 2 more up smashes) up-air, double jump forward air. You can use the tip of up-air (sour-spot) in a juggle to bring Falco back to the ground to combo into up smash again.
Always try to end your combos with f-air and not u-air, because u-air won't kill anyways, but f-air will likely put Falco offstage. When he is off-stage, do the tether character ledgehog, forcing him to land on stage. Punish with a ledgejump down-air, which will spike him into the ground and combo into anything. And the reason I am going into such detail for combos and punishes? Well Falco, just like Fox, dominates the neutral game so hard, that optimizing your punishes when you do manage to hit him really is the key to this matchup. In a 4-stock match, it is not uncommon for me to get 1 zero-to-death on Falco off of a grab. Just grab, blue up-throw, up-smash, juggle a bit til you can land a f-air which puts him off stage, and edgeguard. One trick I like to do to Falco when he is offstage is run towards the ledge but then wave dash backwards. This will bait Falco into using side-B on stage because he thinks you are going for the ledge. When you read his side-b onto stage punish it with down smash. If you know or think Falco is going to offstage firebird to get back, then do a decisive run-off-stage f-air before the up-b activates (Easy to do because unlike Fox, Falco's up-b has no hitbox while charging, and it has a smaller distance).
Purple Pikmin: acquiring 2 of these bad boys will make this matchup MUCH easier, if you are so lucky. Lasers knock back pikmin when thrown, but when you throw 2 pikmin in a row, the 2nd one will make it through. (This applies to Fox as well) You can use 2 subsequent purple tosses (preferably after a hop) to lock down falco and get a free in on him.
When Falco is in on you, your best OoS options are just roll away, or N-air. Assuming the Falco plays perfectly, you'll never shield grab him. If you want to go for a shield grab, be my guest, as the reward for landing a grab is tremendous.
If Falco is laser camping, don't be afraid to spend some time to camp yourself and get a better pikmin lineup (this is what I do). His lasers don't do much damage at all, so spend some time to throw pikmin you don't want offstage. In this matchup, you want Purples, Blues (up-throw can start combos at low percents, and back/forward throw easily gets him offstage), and yellows (immune to lasers, shine won't get them off when latched on either). White pikmin deserve a special note, because their up-throw will easily combo into a forward air at high percents, and purple pikmin are ordered after whites, so landing a white grab at around 80% or higher will usually result in a kill.
For neutral: Stay mobile. Get good at powershielding lasers. When you have a purple, short hop toss it and go for a safe approach. When you have a yellow pikmin, throw it from the ground, run forward, and space yourself to grab falco's landing (he will expect to be safe from the short hop laser but the yellow will have absorbed it).
I feel like I could write much more, but this is already approaching TLDR territory and beyond. If some of this is obvious I apologize.