Bring a box of chocolates?
Similar situation: Our kitten got lost for six days, drama, visits to all vets within 10miles to chat with receptionists and hand out flyers, plastering posters (with less personal details) visibly on neighborhood street furniture like telephone poles, ... And eventually during lunch in the city centre a phonecall from a vet quite far away [to the name+number in the IDchip -- so all those vet-visits were pointless] that somebody had brought him in. So! On a jog to the car I passed an upmarket chocolate shop and bought a decent box (time cost: 3min) and went to pick him up.
For another cat that got lost (2002? Before ID chips anyway), from phonecall I knew a female pensioner: I picked up (without much thinking, clearly!) a hand-made bowl I'd just bought (among other things) from an artisan in Japan. I'm not sure it is/was as much appreciated as I missed it; I had bought a pair, gave the other to a friend.
Note that "missing cat" posters often mention financial rewards, as if that's a motivation to go look for it. Or if you found it, £50 offered will sway you from keeping it (at least £300/year) or kicking it out without phoning.
Motivations: I would feel awkward being offered money to bring back a cat. On the face of it, your phone is much less personal than my family member --- but considering all the personal photos etc on it so it's similar.
I'd be somewhat insulted being offered money for doing the obvious, decent thing.
BUT I'd expect some sort of gesture beyond words of thanks, but what amount of money? 10% of new-value, more/less? The value of the data [time spent on reinstalling after remote wiping etc, risk of ID theft] is higher than the value of the thing. Cash to you (poor student? extremely rich lady-that-lunches?) has different value than to me (middle age, middle income)... so figures are hard.
I've found a phone on a market (say 2005 -- a dumb Nokia, no photos/email/data) and waited 15min to give it back. I WOULD have appreciated being offered (the cash for) a coffee there (cold! windy!), but would have refused anything more.
Choice considerations: "A bottle of wine" is ruled out because a good chance your finder is a Muslim, ex-alcoholic, underage (can't judge on phone!), health-fascist, or otherwise tee-total. And else choice would be hated both by a wine snob and a beer-swilling anti-snob.
So a bunch of flowers can be a good choice for a (female?) finder --- but still can be awkward (allergies! flower-hater!); I'd say half the men would appreciate it. But depends on a nice florist at hand. And finder may be on their way to an evening work do, or long commute, etc... so wilting or having to give it to their host.
Along the same lines, don't bring fresh squid.
(Even if allergic to chocolate, a box is appreciated AND can be passed on as it keeps a few days/weeks.)
Maybe cash after all?: Of course you'd want to retrieve the phone fast as possible (don't lock the finder into their home!), so cash is reasonable if nothing else at hand --- don't start a GreatBritishBakeOff showstopper to give.
But then at least verbally turn it into a thing/gift (like the "here, have a coffee" in my market scenario above; "beer money" is an expression in many languages; ... ).