The only difference between a full certification test (which may well fail) and a 'quick look' session (sometimes called pre-compliance testing) where you go and test stuff, experiment with fixes etc. is the lab's level of liability for the results.
The latter method - just booking some time to do whatever you need can be a very productive use of lab time - you generally get an operator/engineer who has a lot of experience and can quickly identify areas that need attention and suggest fixes. They typically have big assortments of filters, shielding products etc. - I imagine EMC component companies supply these to test houses free, as if something from the kit fixes a problem chances are it will get designed in.
You can try fixes and then get test results that are no different to those that appear in a formal full test report from a product test, and can use these as supporting documentation in a technical file. And you can also test as many things as time permits. e.g. for small products you can test multiple items simultaneously for radiated susceptibility.
Many tests can take quite a while to scan through the frequency range. If you have multiple products, or multiple copies, you can be doing things like applying fixes etc. one one while another is being tested.
A good strategy is to design in multiple approaches to filtering, shielding etc. test the belt-and braces version, and if it passes, then test the effects of removing stuff, swaping to cheaper filters etc. in order of cost to see how necessary and effective each measure is
oh, and always leave ESD and surges til last, as these might kill your device, so you can't do any more testing & have wasted the rest of the day. Where possible take plenty of spare units - you don't want to be spending valuable test house time fixing up dodgy protptypes.
Similarly make sure you have enough software funtionality built in to make testing efficient - excersising hardware, giving clear indications of issues for immunity, having the ability to quickly and easily change things that may affect performance - clck rates, drive strengths, PLL frequencies etc.
With uncalibrated equipment? forget it.
And for radiated, outside an anechoic chamber, forget it. There's way too much ambient junk to get meaningful results even with proper EMC test gear.
Conducted is probably more doable, with a LISN and spectrum analyser as frequencies are low and shielding less of an issue.
What kind of product are you designing?
determining which standards are applicable can be at least as hard as any technical challenge. test houses can advise but are not exactly independent as they will tend to err on the side of including standards & tests