Preheat an outdoor grill for high heat and lightly oil the grate. Close cover.
Combine cherry tomatoes, olive oil, shallot, tapenade, salt, basil, thyme, and pepper in a bowl; mix well.
Lay out foil on a work surface, shiny side-up. Place each salmon fillet skin side-down in the center of a piece of foil. Cover each piece of salmon with 1/4 of the cherry tomato mixture. Fold up the edges of the foil over the salmon to create a parcel, making sure to seal the edges well.
Turn down the heat of the grill and carefully place the foil parcels on the grate. Close the cover and cook until salmon is pale pink in the center and flakes easily with a fork, 7 to 8 minutes. Remove parcels and let them sit for a few minutes before opening.
