For a set L of lines of PG(n,q), a set X of points of PG(n,q) is called an L-blocking set if each line of L contains at least one point of X. Consider a possibly singular quadric Q of PG(n,q) and denote by S (respectively, T) the set of all lines of PG(n,q) meeting Q in 2 (respectively, 1 or q+1) points. For L∈{S,T∪S}, we find the minimal cardinality of an L-blocking set of PG(n,q) and determine all L-blocking sets of that minimal cardinality.