I do the same thing and fold there in that situation. It's a lot easier when you get a flop like this:

Party Poker No-Limit Hold'em, $2 BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

SB ($217.50)
BB ($49.68)
UTG ($91.38)
MP ($200)
CO ($55.36)
Hero ($207.30)

Preflop: Hero is Button with J, J.
UTG calls $2, MP calls $2, 1 fold, Hero raises to $9, 2 folds, UTG raises to $29, MP folds, Hero calls $20.

Flop: ($63) J, Q, J (2 players)
UTG bets $26, Hero calls $26.

Turn: ($115) 7 (2 players)
UTG calls $91.38 (All-In), Hero calls $36.38.

River: ($187.76) 4 (2 players, 1 all-in)

Final Pot: $187.76

Results:
UTG has Qh Kc (two pair, queens and jacks).
Hero has Jd Jh (four of a kind, jacks).
Outcome: Hero wins $242.76.

JJ was my lone bright spot today. I was 13 for 13 with them for 8.37 BB/Hand. Hopefully my Jacks stay hot at...100NL because that's where I'm heading. I had my worst day ever today, losing just under $1k. So I'll bring back this thread when I make it back to 200NL.