Tim writes:

If you don't know you shouldn;t be filing IFR. Period. You can get
someone (including yourself killed.)

If you know, you should explain the answer here. If you don't, why bother
with the melodramatic lecture?

I'll assume that you don't know, and apparently nobody else here knows and
nobody can be bothered to look it up.

This situation is explicitly covered by FAR 91.185 in the United States, which
reads as follows:

==
Part 91 GENERAL OPERATING AND FLIGHT RULES
Subpart B--Flight Rules
Instrument Flight Rules

Sec. 91.185

IFR operations: Two-way radio communications failure.

(a) General. Unless otherwise authorized by ATC, each pilot who has two-way
radio communications failure when operating under IFR shall comply with the
rules of this section.

(b) VFR conditions. If the failure occurs in VFR conditions, or if VFR
conditions are encountered after the failure, each pilot shall continue the
flight under VFR and land as soon as practicable.

(c) IFR conditions. If the failure occurs in IFR conditions, or if paragraph
(b) of this section cannot be complied with, each pilot shall continue the
flight according to the following:

(1) Route.
(i) By the route assigned in the last ATC clearance received;
(ii) If being radar vectored, by the direct route from the point of
radio failure to the fix, route, or airway specified in the vector
clearance;
(iii) In the absence of an assigned route, by the route that ATC has
advised may be expected in a further clearance; or
(iv) In the absence of an assigned route or a route that ATC has
advised may be expected in a further clearance, by the route filed
in the flight plan.

(2) Altitude. At the highest of the following altitudes or flight levels
for the route segment being flown:
(i) The altitude or flight level assigned in the last ATC clearance
received;
(ii) The minimum altitude (converted, if appropriate, to minimum flight
level as prescribed in Sec. 91.121(c)) for IFR operations; or
(iii) The altitude or flight level ATC has advised may be expected in
a further clearance.

(3) Leave clearance limit.
(i) When the clearance limit is a fix from which an approach begins,
commence descent or descent and approach as close as possible to
the expect-further-clearance time if one has been received, or
if one has not been received, as close as possible to the estimated
time of arrival as calculated from the filed or amended (with ATC)
estimated time en route.
(ii) If the clearance limit is not a fix from which an approach begins,
leave the clearance limit at the expect-further-clearance time if
one has been received, or if none has been received, upon arrival
over the clearance limit, and proceed to a fix from which an approach
begins and commence descent or descent and approach as close as
possible to the estimated time of arrival as calculated from the
filed or amended (with ATC) estimated time en route.
==

So the (partial) answer is: Continue with the assigned heading, and maintain
altitude as in (c)(2) above. Part (c)(2)(ii) should keep you above terrain
(FAR 91.177). This still leaves some unanswered questions, though. If you
are given a heading without a fix, and the heading does not intercept your
flight plan or any approach or any expected routing, where do you go? In VMC
you are clearly expected to go VFR and land. In IMC, what do you do?

--
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