Jean Campbell, 53, was last seen heading towards Cranhill Park with her German Shepherd in Glasgow's East End on December 13.
Paul Ward, 21, from Glasgow, appeared at Glasgow Sheriff Court charged with her murder.
Thomas Leyden, 22, also from the city, was charged with attempting to pervert the course of justice.
He also faced a charge under the Misuse of Drugs Act.
Both men made no plea or declaration and were remanded in custody.
The case was continued for further examination and they are due back in court later this month.