During non-Peak and non-Holiday weekends (Valentines and Mother's Day where the holiday falls on a Sat., Sun., or Monday are possible exceptions), centers will deliver EAM (Early AM) packages before or on the commit time of 9:30 am and Next Day Air packages before or on the commit time of noon.
There is a way to get around this. You can use their Express Critical Care Packages service for urgent deliveries, an exclusive, costly service that you can request time-sensitive shipments. This service only operates within the US.
Ground, three-day Select, and 2nd Day Air service packages are not delivered on Saturdays.
Related: How Late Does USPS Deliver? A Complete Guide
Note: UPS is testing the viability of delivering all delivery service levels (Ground, 3 Day Select, 2nd Day Air) on Saturdays in some select cities across the country. Delivery times in those test cities will vary depending on package volume and the available drivers' percentage.
Recommended: Why Did My UPS Package Get Rescheduled?