So training and certification are always the double edged sword for both the employer and the employee.
Let's start with the employer. So as an employer, you want to keep your technical folks as up to speed as possible. As technologies change you want your team to keep pace. To do that you have to arrange for formalized training or just hope they are going to learn it on their own. It is almost always better to at least allow for the team leads to get the formal training and pass down the information on the job to the junior staff. You do need to include some of the junior staff as well so that they feel like they are getting some direct benefit from the classes as well.
Some of the issues that come with training are the cost of the training itself, who gets to go (as often not everyone can go and not everyone is of the skill level to get the most out of the training), how to arrange the coverage at work (time off) for those attending the class and so on. All of this is perpetual too; new technologies are always coming out and then there are always additions to the team in the form of new hires and transfers.
Once classes are taken sometimes there are certifications to earn. It may be that the employee wants this or the employer or it may be a dual interest.
So then the rub - the employee feels that they are now more valuable and hence deserving of a larger salary. They are not wrong about this but they need to take a pragmatic look at it. If the employer effectively paid for the week of training and the certification exam and granted the time off (effectively) to attend the class all of that needs to be calculated before one just randomly goes in to ask for more salary.
It would be my suggestion to consider the output of the company for the classes and the exam first. There is a cost associated with that; if the company paid for it then the employee should consider that investment and the company's desire to boost productivity which helps their bottom line.
A good way to approach this is to review how you put the training and the certification to use. Did it allow the company to do warrantee work they were not able to do before? If so, by you getting certified you are helping the company's bottom line. By learning additional troubleshooting or operational support and product skills in the classes did it allow the company to reduce its service agreement for vendor support (thus saving them money)?
You can base your argument for more salary approaching it like that AFTER proving some worth (think six to twelve months down the road).
Some employers simply look at the negatives only - "if I get them training and they get themselves certified I either need to pay them more or they leave to a company that is going to offer them 20% more in pay and benefits."
So yes, this is always a risk. If your business could increase productivity and earn 20% more for the corporate coffers I am sure the company would go that route. Individuals are no different - if they can increase their own skills and demand more salary they are going to try.
Businesses may be investing in the individual by paying for the classes and the certifications but the individuals are investing the time and effort that goes along with attending the class and trying to prepare for the exam and a lot of that can take place after hours and on their own time.
The smart way for a business to manage this investment is to clearly outline the costs of the classes and the certification training. In doing so the employee understands what the company is spending in their investment of that training for them. The company can also put a clause in that states if the employee wants to take the training and certification that they must stay with the company for 365 days after the class ends or the company has the right to collect the costs of the training from the employee upon a voluntary separation. That is, if the employee wants to chase a raise and leave the company they are going to need to pay for the classes they took. There can be clauses in there too for things like company downsizing, spousal relocation which forces them to move, and so on where the employee wouldn't be forced to pay back for the class. The spirit of a provision like that is so an employee doesn't take advantage of a liberal corporate training policy and then go off and take a competing job offer elsewhere.
The best way for a business to manage a situation where a worker is offered a competitive salary elsewhere is to offer a raise / promotion that allows for a competing pay raise. If the person is shopping around (and is worth keeping) and is getting offers of 15% more in pay and some more flex time you could counter with an 6% or 7% promotional raise and tie it to a 1% or 2% evaluation six months down the road and perhaps also offer the additional flex time as well. It is not the same increase that the competitor is offering but for the convenience of staying put and not having to adjust to a new workplace and so forth I am certain most employees would take it.
I often hear employers / managers grumbling and complaining about lack of employee loyalty when they need to deal with scenarios like this and that the employee shouldn't be asking for salary jumps like that because another job offer came along. I always stop them and remind them that the workplace today is not our grandfather's workplace of years ago. In a majority of the cases the employers, especially very large corporate ones, don't care about the employees anymore than the employees care about the employer when it comes down to dollars and cents. A business is just as quick to relocate to another state and unemploy many of their local workers all for tax breaks and lower salaries. I ask where is the loyalty there and I always get "sometimes things like that are just good business." I never let them have that cake and eat it too. I tell them, if it is in the best interests for the company to make smart business decisions then it is equally evident that the employee should do that on behalf of themselves as well.
Finally there is the scenario where the employee is paying for everything themselves and investing their own time (weekends, holidays, vacation time, etc.). In a situation like that, all bets are off. They person footing all the bill themselves is certainly going into it with the intention of making themselves more valuable to their employer and if that employer doesn't see it that way and doesn't respond reasonably then another simply will.
Losing self starting employees like that is the worst mistake a company can make in my opinion. That is born and breed of someone; you can almost never teach anyone work ethic like that. If that is found in an individual it is worth compensating heavily for it simply because it is such as rare commodity.