The supernova remnants G 5.4-1.2 and G 8.7-0.1 each have a 15 000 yr o
ld pulsar projected along their outside edges. If these are true pulsa
r-supernova remnant associations then the implied pulsar transverse mo
tions for PSR1757-24 and PSR 1800-21 are excessively large ( 1500-2500
km s-1). We present new radio observations made at the VLA in the con
tinuum at 327 MHz and the H i line at 1420 MHz to address this issue.
For G 5.4-1.2 we better constrain the true extent of the remnant and i
ts shape. We also derive an H I absorption distance and the spectral i
ndex distribution across the bright western side of the remnant. All t
he available evidence suggests that G 5.4-1.2 and PSR 1757-24 are asso
ciated. Our deep 327 MHz image of G 8.7-0.1 reveals faint extensions o
f the remnant but no new emission is seen near PSR 1800-21. A possible
new supernova remnant is also discovered north of G 8.7-0.1. Several
difficulties are presented for the proposed association between G 8.7-
0.1 and PSR 1800-2 1, the most serious of which are the lack of a puls
ar-powered nebula and the discrepant distance estimates for the pulsar
and supernova remnant. We conclude that PSR 1800-21 is a foreground o
bject, unrelated to G 8.7-0.1.