On Monday, the stars were seen separately at Mimi's New York apartment, where she lives with the couple's three children, Cooper, 10, Tallulah, seven and five-year-old Willa.
Justin was the first to arrive. He covered his face with a black scarf, dark sunglasses and a baseball cap as he made his way inside the West Village building.
"Justin is totally broken up about losing Phil," a source told US Weekly. "He's doing his best to provide some comfort to Mimi and the kids. He can't believe this happened."
Blue Jasmine star Cate, who starred with Philip in The Talented Mr Ripley, was seen looking sombre as she trekked through the snow to the apartment. She carried in her arms a boxed telescope and a bag of what appeared to be toys for Philip and Mimi's children.
Oscar-winner Philip, 46, was found dead in his New York home on Sunday. It is thought that the late actor, who checked into rehab last May after relapsing from 23 years of sobriety, died of a heroin overdose.
The Wall Street Journal repots that Philip and costume designer Mimi were estranged at the time of his death. His friends and family were said to have become concerned when he failed to pick up his children on Sunday.
"We are devastated by the loss of our beloved Phil and appreciate the outpouring of love and support we have received from everyone," his family said in a statement.
"This is a tragic and sudden loss and we ask that you respect our privacy during this time of grieving. Please keep Phil in your thoughts and prayers."