"with reserve" is correct in written English and can be used in many different contexts.
For example, "He accepted the invitation with reserve." This implies that he accepted the invitation reluctantly.
With Reserve, users provide the date and time window for their reservation, then the app will provide a list of recommendations.
Many have dispensed with reserve requirements altogether.
Sita has been talking -- with reserve.
Sometimes he tries to express it with reserve.
"Don't give it a thought," Briggs said with reserve.
They viewed much of the Old Testament with reserve; some of them rejected it altogether.
Three other bids were accepted with reserve, meaning Seaboard could later reject them.
Ramona bore these slights sometimes with reserve and sometimes with indignation.
The unravelling is the more disturbing for being treated with reserve.
Dr. Schaller and colleagues left six camera traps with reserve managers.
Not only did they speak sense but they spoke it with patience and with reserve.
