During negotiations should I simply ask for them to match? I don't want them to think I'm actively looking for a new job but want to get paid my worth.
At the end, I simply said 'Something I want to bring up is that I've looked at the market and I don't feel I am being paid adequately for the value I'm creating'. I'd be lying if I said it wasn't an awkward conversation. I didn't mention any number at all & was actually met with a slightly negative response, but a week later at the next 1-on-1, it was brought up again & I was awarded a 10% cash raise (I negotiated some ISO's too).
In your scenario, I wouldn't tell them that you interviewed at a competitor either. You can simply tell them that you've looked at other roles & determined market rate as being higher than what you're currently paid. Only use another offer as leverage if you are prepared to leave & take that offer.
Modesty aside, I'll also admit that I'm a high performer in our team & so I already knew that I had leverage. Something I've learned though is that unless you bring it up, it's never going to happen - there is no-one looking out for you unfortunately, so take the initiative & help yourself where you can - it equates to hundreds of thousands of dollars over your career.
However, just because you have a lower likelihood of success, it doesn't mean you shouldn't ask. If you receive a 'No', it will probably speed up the inevitable decision of whether you actually want to stay with this company (knowing that they aren't going to incentivise your performance).
I would also keep in mind that you should only be asking if you either feel you're being paid lower than market or that you've taken on more responsibility so now your wage doesn't adequately match your role. Just asking periodically without a reason isn't going to work for anyone.
Another possibility, is that you've stopped increasing your value to the company. This is normal. Einstein probably wasn't reading patents any faster at 7 years than he was at 3 years when he worked at the patent office.
More importantly to you, the company may not be a place where you can "up your game" any further. You need to seek out new jobs where you can increase your knowledge and value.
A problem for many people is that it's hard to compute their exact value, or they are afraid to have that kind of discussion.
If you're being paid $75k a year, and you've added a significant amount to the bottom line, I doubt you'll have a hard time negotiating a $10-20-30k increase. Same goes for a new job: give them examples of achievements, and show how you were beneficial to the business.
Negotiating a new secondary offer is a great thing to do; it gives you additional leverage. If there's a chance a value creating employee will leave, there is no reason not to give a raise. You could use that offer to negotiate a 25-35% increase, if you can show the value you've created at your current company.
To put it bluntly, most employees are actually not worth that much. They get hired at the least amount possible, and they execute strategies, for the most part, set by a few people who are paid significant amounts.
I also like this Quora post: http://www.quora.com/What-kind-of-jobs-do-software-engineers.... Check out the first answer written by Amin Ariana; it explains things well.
The trick is, make them think you are not looking, but that others are looking at you.
But you have to have the offer in-hand, and you have to be willing to pull the trigger.