Parcel logistics services play a vital and growing role in economies worldwide, with customers demanding faster delivery of nearly everything to their homes. To move larger volumes more cost effectively, express carriers use sort technologies to consolidate parcels that share similar geographic and service characteristics for reduced per-unit handling and transportation costs. This paper focuses on an operational planning problem that arises in two-stage sort systems operating within parcel transportation networks. In this context, primary sorters perform an initial grouping of parcels into "piles" that are subsequently dispatched when necessary to secondary sorters; there, each pile's parcels are fine-sorted based on their loading destinations and service class for final packing into outbound transportation vehicles. Such systems must be designed to handle a high degree of uncertainty in the quantity and timing of arriving parcels, yet must also group and sort the parcels to meet tight departure deadlines. Thus motivated, we propose robust planning models that assign parcels to sort equipment while protecting against different sources of demand uncertainty commonly faced by parcel carriers. We demonstrate the computational viability of the proposed models using realistic-sized instances based on industry data, and show their value in providing sort plan alternatives that trade off operational costs and levels of robustness.