In Augusta, Mr. Kilmer usually creates a temporary lounge on parents’ weekend for the pilots and flight attendants who must wait for their clients to return from their children’s camps, so that they can depart later that afternoon. He has already received catering orders for return flights, which include fruit and sandwich trays for adults and sandwich boxes for younger siblings. One flier has already requested a peanut butter and jelly sandwich, a fruit cup with a single strawberry, a juice box, a banana and a cookie or brownie.

The popularity of private-plane travel is forcing many high-priced camps, where seven-week sessions can easily cost more than $10,000, to balance the habits of their parents against the ethos of simplicity the camps spend the summer promoting.

Kyle Courtiss, whose family runs Camp Vega in Maine, said that his staff was trained “to be cognizant of stuff like that” and that private planes were “not what this camp is about.”

Some camps said they recognized that the parents who flew in private planes were often strong financial supporters of these camps. Arleen Shepherd, director of Camp Skylemar, in Naples, Me., said that while some of the high-profile parents whose children attend Skylemar might fly privately, some campers had never flown on a plane.

Private-plane companies and parents say these flights have also become more affordable to a broader base of fliers.