On rainy days, Lauren Kope pores over stacks of century-old garden plans, pondering the past. Ms. Kope, 30 years old, works as rosarian for Wyck Historic House and Garden in Philadelphia, where she catalogs and tends to the nation’s oldest continuously preserved rose garden, which dates to 1824.

Ms. Kope has immersed herself in the lore and history of the garden’s various cultivars, which include rarities such as the hybrid “Lafayette” rose, planted in honor of the Marquis de Lafayette’s visit to the house in 1825. Though...