Was there anything in particular you felt he was predicting and punishing on? As a fellow Link main maybe I can offer my view of the match-up.
Ness has a speed, air speed, *and* frame advantage, so Links should be playing the poke and zone game to get Ness to commit to something like a smash attack, then rush in with a dash attack, grab, or dtilt to fair. (i.e. bait laggy moves) Arrows work well to interrupt Ness's projectile use. If you're an agile Link player, it should be trivial to jump past Ness's projectiles or otherwise disable them (nairing PK Thunder for example), then you can overwhelm Ness with Link's superior range and hitbox coverage. Link's air kit is amazing in terms of knockback, so despite Ness having better maneuverability in the air, Link still has a range, weight, and power advantage.
PK Fire is one of Ness's more reliable combo starters. I think it goes under Link's shield now (even while crouched), it's stupidly low to the ground. Most Ness players will follow it (if it connects) with fsmash or upsmash. If you use SDI (smash DI, repeatedly tapping the stick in the direction you want to go to wiggle out of multi-hit moves), it'll help you stay out of PK Fire combos.
I've run into problems using Link's bombs against Ness or Lucas. PK Fire can reach you fast enough (on reaction) that throwing your bomb will still detonate close enough to hurt you. If you must use bombs, throw them vertically or z-drop to surprise the Ness player. (i.e. don't throw immediately after drawing) PK Fire's a pesky enough projectile that you can't play threat-zone games with the bomb without risking harm to yourself, since PK Fire has good range and is hard to block with an attack due to its low profile. Up-B OoS is good here, if Ness is close enough.
Other than that, Link has a melee advantage (disjointed hitbox ftw) and projectile advantage. Ness can win the jab game due to fewer recovery frames and his multi-hit moves tend to interrupt Link's melee game. Ness can't absorb anything except the bomb's explosion, though, so it's not reliable for him in this match-up.
If you have any specific scenarios in mind I'd love to think about them. I play against a Ness main on a semi-regular basis and I need the practice.#ssbu