There is now one, small backpacker’s camp on the edge of the reserve, accessed from Etsha 6, on the Panhandle road:

Makwena Camp (camping only)
This small, budget camp is reached about 14km from Etsha 6 on the Panhandle – usually 12km of 4WD track from the road, followed by a 2km boat ride. These 4WD transfers to/from Etsha 6, if you can organise them, are P100 per person return.
Makwena is currently being run as a campsite for budget travellers, and charges P33 per person per day for camping. From there a boat transfer to a fly-camp on an island is P100 per person (return), from where you can hire mekoro for P100 per day. Each mokoro seats one or two people.
If you want to go for longer than a day then there’s a P300 per mokoro per night ‘sleep-out’ fee, which enables you to stay out on one of the islands; note, too, that there’s an entry fee into this community area of about P25 per person.
If you’re interested then apparently Mr Malcolm Thomas who works in the Co-op supermarket at Etsha 6 can get in touch with the camp from there. However, this didn’t work when I last tried, as he wasn’t around. It’s certainly best to contact the camp at least two or three days in advance, and you will need to arrive with all your food and camping equipment; Makwena cannot supply either.