I think you only way to tell, is by guessing base on color. Orange/tangerine is the color usually associated with beta-carotene, like red and lycopene.

Tasti-lee is a tomato high in lycopene, it's flesh has a uniform really deep red color. Look here (Tasti-lee): https://www.youtube.com/watch?v=09hLWJ6tYJ4

I would guess you would want a uniform rich orange/tagerine colored fruit. The genes are you probably want are B and Del:
Fruit colors:
http://tgrc.ucdavis.edu/Images/B,Del-LA0316,LA2996A-fruit-.jpg
http://tgrc.ucdavis.edu/images/B%5Eog,hp-1,sp,Del,B,t%5Ev,t,u-LA3771,LA3802,LA2996A,LA0316,LA0351,LA3250-fruit-comp.jpg

Genes:
http://tgrc.ucdavis.edu/Data/Acc/GenDetail.aspx?Gene=Del
http://tgrc.ucdavis.edu/Data/Acc/GenDetail.aspx?Gene=B

Here is a link that might be useful: ucdavis genes queries

Thanks for all the link information, I think it will be usefull. You're right, I'd want B and Del as genes.

The problem is that I probably will be using other orange tomatoes in the breeding program I'm looking at starting(Sungold and Husky Gold being likely ones). And since I don't know their genetics (and since a bunch of other genes can cause a tomato to be orange, I was wondering if there were some kind of 'home' tests to determine carotene levels.)

I can see some differences in the photos from ucdavis between the different genes, but I think its going to be much harder to determine differences in field conditions (and ucdavis already knows what genes their tomatoes are expressing!!).

Maybe I'll have to think carefully on how to build my breeding program.

Yea, it's going to be a problem without testing. Sorry, not much help and it's probably just B(not Del, my bad) that you'd want.

I find this interesting, I'm not claiming to be knowledgeable in this stuff, but it seems to me B gene is dominant. So, shouldn't you still get a good amount of beta-carotene in an F1 hybrid?
If it's inheritance is co-dominant or intermediate, the resulting hybrid may still show a good amount of beta-carotene compared to the non-B gene carrying parent.

Using non-orange tomatoes as a parent may probably be best if you want to breed the line further.

Also, have you tasted Caro Rich, if so, how was the flavor? How does it compare to Sungold?

I haven't tasted Caro Rich (I've heard mixed reviews on it). However I was interested in it because my goal is to bread a 'healthier' tomato, in that though lycopene (the carotenid that makes tomatoes red) is an anti-oxidant it is not a vitamin. Yellow and orange tomatoes provide beta-carotene, which is a anti-oxidant and a 'safe' vitamin A (you can o.d. on Vit. A, but your body only converts the amount of beta-carotene to vitamin A that it needs. I thought if I bred it to good tasting tomatoes, I could overcome any problems w/ flavor (unless any off flavors are tied to the extra beta carotene).

Any F1 Hybrid w/ Caro should still have a good amount of beta carotene. I was trying to see if there was a way I could differentiate between different 'oranges'

Oh, i see.
Well, good luck.

Actually if your goal was to increase beta-carotene do not use Delta. Just work with B. Cross it to red or yellow "r" types and it will clearly segregate for you. You won't need testing to know it's there. The only issue would be crossing with the orange tangerine gene based tomatoes. Unless you get stock from TGRC, Almost all orange tomatoes you could easily obtain will be the tangerine gene. Even still, Beta effects flavor so much it should be pretty evident. Visually when crossing with reds, even the intermediate types clearly stood out in F2's when I was working with it.

The flavor is a big issue.

If you want fairly decent Beta-carotene material you may inquire Dr Stommel at the USDA who released lines somewhere about 2000. I know one that comes to mind is 97L97. This material is in a processor type background not fresh market type. If you search google for Stommel, USDA, Beta you will find release notices and contact information.