I am growing over 5 vine sorts of honeysuckle, here in zone 7, and only Lonicera periclymenum seems fragrant. I am growing L. periclymenum 'G.S.Thomas' but L. p. serotina seems to be more commonly sold.
L. tragophylla has bloomed, but I notice no odor, and L. sempervirens sorts are well known to be odorless, as is the recently promoted 'Mandarin'.
No one could convince me to plant the fragrant and vigorous 'Hall's Prolific' type of L. japonica. The common sort of L. japonica is the most unbelievable pest here.
My acid, sandy soil seems to limit the vigor of L.tragophylla,tellmanniana, 'Mandarin, and periclymenum.
L. sempervirens sorts thrive and L.japonica is a total weed.

Lonicera sempervirens is a beautiful vine that flowers heavily and is non-invasive. I'm not aware of any significant fragrance, but the hummingbirds and butterflies love it. Confederate or star jasmine has a nice fragrance and is non-invasive, but probably would not be hardy in Ohio.

Thanks to both of you. The Hall's honeysuckle is commonly sold in nurseries around here, even though it is on the invasive list for Ohio. Too bad we can't get that wonderful fragrance elsewhere. I will look for sempervirens. You are right, dawgie, jasmine will not live here.

You might like 'Goldflame', a beautiful hybrid of uncertain origin that is not invasive, blooms pretty much all summer and has some fragrance. It's quite common in nurseries, too. Sometimes it goes by other names, but you can often tell the characteristic combination of pink-and-yellow flowers and smooth, blue-green leaves.

Stefan

There is a very fragrant bush honeysuckle - Lonicera syringantha - deciduous and easily kept in bounds. If you want a climber, try L. fragrantissima which flowers in mid-winter.

I have Mandarin and Gold Flame growing in my zone 6 garden. Both are completely hardy and not invasive. Mandarin seems to bloom more in distinctive flushes while GF is more continuous. At this writing, Mandarin is a foot higher than the top of the pole, to give you an idea of a year's growth.

Three-year old Mandarin growing up a pole:

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Now, I do like that flush of pink on the mandarin! Beautiful pictures, Harry, thank you!

I appreciate the other recommendations, too. Thanks.