Full Tilt Poker
Pot Limit Omaha Ring game
Blinds: $0.10/$0.25
5 players
Converter

Stack sizes:
UTG: $26.80
CO: $19.10
Button: $28.85
SB: $51.25
Hero: $23.40

Pre-flop: (5 players) Hero is BB with 8 7 9 6
UTG folds, CO calls, Button raises to $1.1, SB calls, Hero calls, CO calls.

Flop: 8 A T ($4.4, 4 players)
SB checks, Hero checks, CO checks, Button bets $4.4, SB calls, Hero calls, CO folds.

Turn: 5 ($17.6, 3 players)
SB checks, Hero bets $17.6, ???

and a second one, same idea --

Full Tilt Poker
Pot Limit Omaha Ring game
Blinds: $0.10/$0.25
6 players
Converter

Stack sizes:
UTG: $23.70
UTG+1: $36
CO: $12.25
Hero: $25
SB: $24.05
BB: $5.60

Pre-flop: (6 players) Hero is Button with Q A T 7
UTG calls, UTG+1 folds, CO calls, Hero calls, SB calls, BB checks.

Flop: T 3 7 ($1.25, 5 players)
SB checks, BB checks, UTG bets $1.25, CO folds, Hero calls, 2 folds.

Turn: Q ($3.75, 2 players)
UTG bets $3.75, Hero raises to $15, ???

Since I'm an Omaha newbie you'll have to take everything here with a big grain of salt but...

Hand 1:
The fact that he led the flop and then checked to you on a seemingly harmless card tells me he's not overly confident in his hand. Maybe 2P, or perhaps overplaying TP? But from his perspective, what would you be playing that you call a pot-sized bet on the flop and then lead out with a large pot-sized bet on the turn when a harmless card falls? It's unlikely that 5h fits with your hand in any meaningful way, so he may just read your move as a semi-bluff.

Hand 2:
Does that really count as a semi-bluff? You've picked up T2P on a fairly uncoordinated board, so the only current threat is a set (3's being the most likely, since you're holding one of each of the others).

I don't even play Omaha but just intuitively I would not bet the turn in that first hand. The Button led the flop with a pot sized bet, and he did not check the turn (the SB did), so he is still left to act. If the SB bet the flop and then checked the turn then sure I may bet, but not with the original bettor still left to act.

Good point, I completely missed the fact that Button was still to act in the first hand.

For hand #1

I shoveled the turn partially because I didn't mind being all in here, and partially for the fold equity it would get me. If he has AA, we're gonna be all in, and depending on what his "xx" are, we could have ≥19 outs. If he DOESN'T have exactly AA though, he's faced with a pretty tough decision.