Despite the severe thunderstorm, which caused widespread power outages; the concert continued as planned.
Correct: C
The phrase 'Despite the severe thunderstorm, which caused widespread power outages' is an introductory dependent clause. After an introductory clause, a comma is required before the main independent clause ('the concert continued as planned'). A semicolon is incorrect here because it is used to separate independent clauses or complex items in a list, not to separate a dependent clause from an independent one. The relative clause 'which caused widespread power outages' is non-essential and is correctly set off by commas. Option C correctly uses a comma to separate the introductory clause from the main clause.