  The Birch and Swinnerton-Dyer conjecture has been numerically verified for
the Jacobians of 32 modular hyperelliptic curves of genus 2 by Flynn,
Lepr\'evost, Schaefer, Stein, Stoll and Wetherell, using modular methods. In
the calculation of the real period, there is a slight inaccuracy, which might
give problems for curves with non-reduced components in the special fibre of
their N\'eron model. In this present paper we explain how the real period can
be computed, and how the verification has been extended to many more
hyperelliptic curves, some of genus 3, 4 and 5, without using modular methods.
