If it's shield pressure, you have a number of options at your disposal. A lot of space animals do early aerials, which give them enough frame disadvantage that they can be shield grabbed. Pay attention to how high they start their aerial, as this will govern whether or not you can shield grab their aerials.
If a spacy up-tilts your shield, chances are they will do it again. You can mash grab and ASDI down Fox's u-tilt until 15%, and Falco's until 22%. When spacies are at higher percents, you can up-b out of shield without being in a bad spot afterward because it will actually throw them far enough away from you. In some situations, though, you have to respect u-tilt and either roll away or wavedash out of shield and reset.
Stomp and nair oos are pretty good options, but you have to time them well, or you will get stuffed. Make sure you jump quickly after shield stun ends.
Another option is to simply double jump away and cover yourself with a stomp, bair, or falling uair. Falco's aerial drift is great, and sometimes jumping over the opponent is not easy for them to deal with (unless they ready you perfectly).